Edit Profile (opens in new tab) Sogge, Christopher D. Compute Distance To: Compute Author ID: sogge.christopher-d Published as: Sogge, Christopher D.; Sogge, C. D.; Sogge, Christopher; Sogge, Chris D.; Sogge, Chris more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 124 Publications since 1985, including 6 Books 1 Contribution as Editor · 2 Further Contributions Co-Authors: 55 Co-Authors with 92 Joint Publications 1,922 Co-Co-Authors all top 5 Co-Authors 34 single-authored 17 Smith, Hart F. 11 Blair, Matthew D. 11 Metcalfe, Jason L. 10 Zelditch, Steve 7 Lindblad, Hans 6 Wang, Chengbo 5 Seeger, Andreas 5 Sire, Yannick 4 Huang, Xiaoqi 4 Keel, Markus 4 Kenig, Carlos Eduardo 4 Stein, Elias Menachem 3 Nakamura, Makoto 3 Xi, Yakun 2 Beltran, David 2 Chen, Xuehua 2 Christ, Michael 2 Fefferman, Charles Louis 2 Hickman, Jonathan 2 Journé, Jean-Lin 2 Lanzani, Loredana 2 Minicozzi, William Philip II 2 Mockenhaupt, Gerd 2 Nagel, Alexander 2 Phong, Duong Hong 2 Pierce, Lillian B. 2 Ricci, Fulvio 2 Ruiz, Alberto 2 Soffer, Avraham 2 Tao, Terence 2 Wainger, Stephen 2 Zhang, Junyong 2 Zhou, Yi 1 Barceló, Bartolomé 1 Beckner, William 1 Bourgain, Jean 1 Christ, F. M. 1 Dafni, Galia 1 Du, Yi 1 Georgiev, Vladimir S. 1 Hezari, Hamid 1 Hidano, Kunio 1 Huang, Shanlin 1 Ionescu, Alex 1 Ionescu, Alexandru D. 1 Kearn, Vickie 1 Knapp, Anthony William 1 Krantz, Steven George 1 Lu, Jianfeng 1 Magyar, Akos 1 Miao, Changxing 1 Mirek, Mariusz 1 Nahmod, Andrea R. 1 Oberlin, Daniel M. 1 Pan, Yibiao 1 Rothschild, Linda Preiss 1 Schlag, Wilhelm 1 Shahidi, Freydoon 1 Shakarchi, Rami 1 Shao, Peng 1 Shokurov, Vyacheslav Vladimirovich 1 Stein, Jeremy C. 1 Stein, Karen 1 Steinerberger, Stefan 1 Stewart, Ann Ann 1 Street, Brian 1 Tohaneanu, Mihai 1 Toth, John Andrew 1 Wang, Xing 1 Widom, Harold 1 Xu, Hang 1 Yang, Jianwei 1 Yao, Xiaohua 1 Zhang, Cheng 1 Zhang, Xiaoyi 1 Zheng, Shijun 1 Zhou, Zhengfang 1 Zhu, Jiuyi all top 5 Serials 10 Mathematical Research Letters 8 Communications in Partial Differential Equations 7 American Journal of Mathematics 6 Duke Mathematical Journal 6 Inventiones Mathematicae 6 Journal of Functional Analysis 5 Proceedings of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Journal of the American Mathematical Society 4 The Journal of Geometric Analysis 3 Communications in Mathematical Physics 3 Journal d’Analyse Mathématique 3 Mathematische Annalen 3 Revista Matemática Iberoamericana 3 Annals of Mathematics. Second Series 3 Cambridge Tracts in Mathematics 3 Analysis & PDE 2 Bulletin of the American Mathematical Society. New Series 2 Discrete and Continuous Dynamical Systems 1 Communications on Pure and Applied Mathematics 1 Arkiv för Matematik 1 Acta Mathematica 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Colloquium Mathematicum 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Japanese Journal of Mathematics. New Series 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Tôhoku Mathematical Journal. Second Series 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Forum Mathematicum 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Séminaire Équations aux Dérivées Partielles 1 Journal of the European Mathematical Society (JEMS) 1 Annals of Mathematics Studies 1 Contemporary Mathematics 1 RIMS Kôkyûroku Bessatsu 1 Cambridge Journal of Mathematics all top 5 Fields 100 Partial differential equations (35-XX) 53 Global analysis, analysis on manifolds (58-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 9 Operator theory (47-XX) 7 Differential geometry (53-XX) 3 History and biography (01-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 3,140 times in 1,606 Documents Cited by ▼ Year ▼ Fourier integrals in classical analysis. Zbl 0783.35001Sogge, Christopher D. 202 1993 On existence and scattering with minimal regularity for semilinear wave equations. Zbl 0846.35085Lindblad, Hans; Sogge, Christopher D. 179 1995 Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators. Zbl 0644.35012Kenig, C. E.; Ruiz, A.; Sogge, C. D. 152 1987 Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds. Zbl 0641.46011Sogge, Christopher D. 127 1988 Weighted Strichartz estimates and global existence for semilinear wave equations. Zbl 0893.35075Georgiev, Vladimir; Lindblad, Hans; Sogge, Christopher D. 126 1997 Decay estimates for Schrödinger operators. Zbl 0743.35008Journé, J.-L.; Soffer, A.; Sogge, C. D. 117 1991 Regularity properties of Fourier integral operators. Zbl 0754.58037Seeger, Andreas; Sogge, Christopher D.; Stein, Elias M. 99 1991 Global Strichartz estimates for nontrapping perturbations of the Laplacian. Zbl 0972.35014Smith, Hart F.; Sogge, Christopher D. 91 2000 Lectures on nonlinear wave equations. Zbl 1089.35500Sogge, Christopher D. 84 1995 Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. Zbl 0776.58037Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 76 1993 Oscillatory integrals and spherical harmonics. Zbl 0636.42018Sogge, Christopher D. 75 1986 Long-time existence for small amplitude semilinear wave equations. Zbl 0869.35064Lindblad, Hans; Sogge, Christopher D. 70 1996 Averages of functions over hypersurfaces in \(\mathbb R^n\). Zbl 0626.42009Sogge, Christopher D.; Stein, Elias M. 63 1985 Wave front sets, local smoothing and Bourgain’s circular maximal theorem. Zbl 0759.42016Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 57 1992 Almost global existence for some semilinear wave equations. Zbl 1031.35107Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 55 2002 Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 53 2004 Lectures on nonlinear wave equations. 2nd ed. Zbl 1165.35001Sogge, Christopher D. 52 2008 On the convergence of Riesz means on compact manifolds. Zbl 0653.35068Sogge, Christopher D. 50 1987 Long-time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods. Zbl 1162.35052Metcalfe, Jason; Sogge, Christopher D. 46 2006 Hangzhou lectures on eigenfunctions of the Laplacian. Zbl 1312.58001Sogge, Christopher D. 45 2014 Riemannian manifolds with maximal eigenfunction growth. Zbl 1018.58010Sogge, Christopher D.; Zelditch, Steve 44 2002 Strichartz estimates for the wave equation on manifolds with boundary. Zbl 1198.58012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 44 2009 Propagation of singularities and maximal functions in the plane. Zbl 0754.35004Sogge, Christopher D. 43 1991 The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators. Zbl 0678.35096Christ, F. M.; Sogge, C. D. 41 1988 On the boundedness of functions of (pseudo-) differential operators on compact manifolds. Zbl 0698.35169Seeger, A.; Sogge, C. D. 41 1989 On the \(L^p\) norm of spectral clusters for compact manifolds with boundary. Zbl 1189.58017Smith, Hart F.; Sogge, Christopher D. 37 2007 On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles. Zbl 1193.35100Hidano, Kunio; Metcalfe, Jason; Smith, Hart F.; Sogge, Christopher D.; Zhou, Yi 37 2010 On the critical semilinear wave equation outside convex obstacles. Zbl 0860.35081Smith, Hart F.; Sogge, Christopher D. 36 1995 Global existence of null-form wave equations in exterior domains. Zbl 1138.35065Metcalfe, Jason; Sogge, Christopher D. 34 2007 Fourier integrals in classical analysis. 2nd edition. Zbl 1361.35005Sogge, Christopher D. 32 2017 Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 29 2002 Strong uniqueness theorems for second order elliptic differential equations. Zbl 0734.35012Sogge, Christopher D. 29 1990 Lower bounds on the Hausdorff measure of nodal sets. Zbl 1242.58017Sogge, Christopher D.; Zelditch, Steve 29 2011 The Strauss conjecture on Kerr black hole backgrounds. Zbl 1295.35327Lindblad, Hans; Metcalfe, Jason; Sogge, Christopher D.; Tohaneanu, Mihai; Wang, Chengbo 28 2014 Bounds for eigenfunctions of differential operators. Zbl 0703.35133Seeger, A.; Sogge, C. D. 28 1989 Hyperbolic trapped rays and global existence of quasilinear wave equations. Zbl 1077.35083Metcalfe, Jason; Sogge, Christopher D. 26 2005 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 25 1997 On Strichartz estimates for Schrödinger operators in compact manifolds with boundary. Zbl 1169.35012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 25 2008 Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions. Zbl 1234.35156Sogge, Christopher D. 24 2011 Strichartz estimates for Dirichlet-wave equations in two dimensions with applications. Zbl 1246.35052Smith, Hart F.; Sogge, Christopher D.; Wang, Chengbo 23 2012 About the blowup of quasimodes on Riemannian manifolds. Zbl 1214.58012Sogge, Christopher D.; Toth, John A.; Zelditch, Steve 23 2011 Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Zbl 1209.35083Du, Yi; Metcalfe, Jason; Sogge, Christopher D.; Zhou, Yi 23 2008 Concerning the wave equation on asymptotically Euclidean manifolds. Zbl 1231.35030Sogge, Christopher D.; Wang, Chengbo 21 2010 A unique continuation theorem for second order parabolic differential operators. Zbl 0704.35016Sogge, C. D. 21 1990 A natural lower bound for the size of nodal sets. Zbl 1329.35224Hezari, Hamid; Sogge, Christopher D. 19 2012 Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary. Zbl 1262.58015Blair, Matthew D.; Smith, Hart F.; Sogge, Chris D. 19 2012 Eigenfunction and Bochner Riesz estimates on manifolds with boundary. Zbl 1017.58016Sogge, Christopher D. 18 2002 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 18 2015 Averages over hypersurfaces. Smoothness of generalized Radon transforms. Zbl 0695.42012Sogge, C. D.; Stein, Elias M. 17 1990 Lower bounds on the Hausdorff measure of nodal sets. II. Zbl 1283.58020Sogge, Christopher D.; Zelditch, Steve 17 2012 Global existence for nonlinear wave equations with multiple speeds. Zbl 1052.35133Sogge, Christopher D. 16 2003 Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains. Zbl 1149.35055Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 15 2005 Maximal operators associated to hypersurfaces with one nonvanishing principal curvature. Zbl 0880.42011Sogge, Christopher D. 15 1995 Negative results for Nikodym maximal functions and related oscillatory integrals in curved space. Zbl 0884.42016Minicozzi, William P. II; Sogge, Christopher D. 15 1997 Oscillatory integrals associated to folding canonical relations. Zbl 0746.58076Pan, Yibiao; Sogge, Christopher D. 15 1990 On eigenfunction restriction estimates and \(L^4\)-bounds for compact surfaces with nonpositive curvature. Zbl 1307.58013Sogge, Christopher D.; Zelditch, Steve 15 2014 A few endpoint geodesic restriction estimates for eigenfunctions. Zbl 1293.58011Chen, Xuehua; Sogge, Christopher D. 14 2014 A note on unique continuation for Schrödinger’s operator. Zbl 0661.35056Kenig, Carlos E.; Sogge, Christopher D. 14 1988 Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms. Zbl 0689.35015Barcelo, B.; Kenig, C. E.; Ruiz, A.; Sogge, C. D. 14 1988 Oscillatory integrals and unique continuation for second order elliptic differential equations. Zbl 0703.35027Sogge, Christopher D. 14 1989 Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds. Zbl 1436.35340Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 13 2020 Nonlinear hyperbolic equations in infinite homogeneous waveguides. Zbl 1078.35076Metcalfe, Jason; Sogge, Christopher D.; Stewart, Ann Ann 13 2005 On Strichartz and eigenfunction estimates for low regularity metrics. Zbl 0832.35018Smith, Hart F.; Sogge, Christopher D. 13 1994 Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions. Zbl 1185.35140Metcalfe, Jason; Sogge, Christopher D. 13 2006 Focal points and sup-norms of eigenfunctions. Zbl 1361.32011Sogge, Christopher D.; Zelditch, Steve 13 2016 Concerning Toponogov’s theorem and logarithmic improvement of estimates of eigenfunctions. Zbl 1394.58016Blair, Matthew D.; Sogge, Christopher D. 13 2018 Averages over hypersurfaces. II. Zbl 0656.42012Sogge, Christopher D.; Stein, Elias M. 13 1986 Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition. Zbl 1098.35112Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Zbl 1213.35314Metcalfe, Jason; Sogge, Christopher D. 11 2010 On integrals of eigenfunctions over geodesics. Zbl 1321.58023Chen, Xuehua; Sogge, Christopher D. 11 2015 Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière. Zbl 1331.58036Sogge, Christopher D. 11 2016 Remarks on global solutions for nonlinear wave equations under the standard null conditions. Zbl 1262.35170Lindblad, Hans; Nakamura, Makoto; Sogge, Christopher D. 11 2013 Concerning Nikodym-type sets in 3-dimensional curved spaces. Zbl 0968.42016Sogge, Christopher D. 9 1999 On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions. Zbl 1330.58023Blair, Matthew D.; Sogge, Christopher D. 9 2015 Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions. Zbl 1321.58029Blair, Matthew D.; Sogge, Christopher D. 9 2015 A sharp restriction theorem for degenerate curves in \(R^ 2\). Zbl 0621.42009Sogge, Christopher D. 9 1987 Concerning \(L^p\) resolvent estimates for simply connected manifolds of constant curvature. Zbl 1303.53052Huang, Shanlin; Sogge, Christopher D. 9 2014 Improved critical eigenfunction estimates on manifolds of nonpositive curvature. Zbl 1386.58014Sogge, Christopher D. 8 2017 Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet theorem. Zbl 1377.35204Sogge, Christopher D.; Xi, Yakun; Zhang, Cheng 8 2017 Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature. Zbl 1428.35248Blair, Matthew D.; Sogge, Christopher D. 7 2019 Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions. Zbl 1377.58026Blair, Matthew D.; Sogge, Christopher D. 7 2017 Concerning the \(L^4\) norms of typical eigenfunctions on compact surfaces. Zbl 1317.58035Sogge, Christopher D.; Zelditch, Steve 7 2012 \(L^ p\) regularity for the wave equation with strictly convex obstacles. Zbl 0805.35169Smith, Hart F.; Sogge, Christopher D. 6 1994 Uniqueness in Cauchy problems for hyperbolic differential operators. Zbl 0763.35012Sogge, Christopher D. 6 1992 Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions. Zbl 0865.35077Lindblad, Hans; Sogge, Christopher D. 6 1996 Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan 5 2019 On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 5 2000 A note on \(L^p\)-norms of quasi-modes. Zbl 1364.35219Sogge, Christopher D.; Zelditch, Steve 5 2016 Lower bounds for interior nodal sets of Steklov eigenfunctions. Zbl 1359.35116Sogge, Christopher D.; Wang, Xing; Zhu, Jiuyi 5 2016 Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Zbl 1376.32011Sogge, Christopher D.; Zelditch, Steve 5 2016 Averages over curves with torsion. Zbl 0934.42008Oberlin, Daniel; Smith, Hart F.; Sogge, Christopher D. 4 1998 On local existence for nonlinear wave equations satisfying variable coefficient null conditions. Zbl 0792.35125Sogge, Christopher D. 4 1993 Fourier integrals in classical analysis. Paperback reprint of the hardback edition 1993. Zbl 1143.35002Sogge, Christopher D. 4 2008 Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials. Zbl 1472.35257Blair, Matthew D.; Sire, Yannick; Sogge, Christopher D. 4 2021 \(L^ p\) estimates for the wave equation and applications. Zbl 0796.35111Sogge, Christopher D. 3 1993 \(L^ p \to{} L^{p'}\) estimates for time-dependent Schrödinger operators. Zbl 0751.35011Journé, J. L.; Soffer, A.; Sogge, C. D. 3 1990 Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary. Zbl 1393.35016Sogge, Christopher D.; Zelditch, Steve 3 2017 On multilinear spectral cluster estimates for manifolds with boundary. Zbl 1146.58019Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 3 2008 Null form estimates for \((1/2,1/2)\) symbols and local existence for a quasilinear Dirichlet-wave equation. Zbl 1016.35008Smith, Hart F.; Sogge, Christopher D. 2 2000 Smoothing estimates for the wave equation and applications. Zbl 0901.35050Sogge, Christopher D. 2 1995 Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials. Zbl 1472.35257Blair, Matthew D.; Sire, Yannick; Sogge, Christopher D. 4 2021 Sharp local smoothing estimates for Fourier integral operators. Zbl 1494.42013Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 2 2021 Weyl formulae for Schrödinger operators with critically singular potentials. Zbl 1477.58021Huang, Xiaoqi; Sogge, Christopher D. 1 2021 Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds. Zbl 1436.35340Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 13 2020 Analysis and applications: the mathematical work of Elias Stein. Zbl 1452.32001Fefferman, Charles; Ionescu, Alex; Tao, Terence; Wainger, Stephen 1 2020 Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds. Zbl 07269819Sire, Yannick; Sogge, Christopher D.; Wang, Chengbo; Zhang, Junyong 1 2020 Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature. Zbl 1428.35248Blair, Matthew D.; Sogge, Christopher D. 7 2019 Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan 5 2019 The Strauss conjecture on negatively curved backgrounds. Zbl 1428.35231Sire, Yannick; Sogge, Christopher D.; Wang, Chengbo 2 2019 Concerning Toponogov’s theorem and logarithmic improvement of estimates of eigenfunctions. Zbl 1394.58016Blair, Matthew D.; Sogge, Christopher D. 13 2018 On instability of the Nikodym maximal function bounds over Riemannian manifolds. Zbl 1440.42091Sogge, Christopher D.; Xi, Yakun; Xu, Hang 2 2018 Fourier integrals in classical analysis. 2nd edition. Zbl 1361.35005Sogge, Christopher D. 32 2017 Improved critical eigenfunction estimates on manifolds of nonpositive curvature. Zbl 1386.58014Sogge, Christopher D. 8 2017 Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet theorem. Zbl 1377.35204Sogge, Christopher D.; Xi, Yakun; Zhang, Cheng 8 2017 Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions. Zbl 1377.58026Blair, Matthew D.; Sogge, Christopher D. 7 2017 Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary. Zbl 1393.35016Sogge, Christopher D.; Zelditch, Steve 3 2017 Localized \(L^p\)-estimates for eigenfunctions. II. Zbl 1390.58019Sogge, Christopher D. 1 2017 Focal points and sup-norms of eigenfunctions. Zbl 1361.32011Sogge, Christopher D.; Zelditch, Steve 13 2016 Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière. Zbl 1331.58036Sogge, Christopher D. 11 2016 A note on \(L^p\)-norms of quasi-modes. Zbl 1364.35219Sogge, Christopher D.; Zelditch, Steve 5 2016 Lower bounds for interior nodal sets of Steklov eigenfunctions. Zbl 1359.35116Sogge, Christopher D.; Wang, Xing; Zhu, Jiuyi 5 2016 Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Zbl 1376.32011Sogge, Christopher D.; Zelditch, Steve 5 2016 Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces. Zbl 1364.58016Miao, Changxing; Sogge, Christopher D.; Xi, Yakun; Yang, Jianwei 2 2016 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 18 2015 On integrals of eigenfunctions over geodesics. Zbl 1321.58023Chen, Xuehua; Sogge, Christopher D. 11 2015 On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions. Zbl 1330.58023Blair, Matthew D.; Sogge, Christopher D. 9 2015 Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions. Zbl 1321.58029Blair, Matthew D.; Sogge, Christopher D. 9 2015 Hangzhou lectures on eigenfunctions of the Laplacian. Zbl 1312.58001Sogge, Christopher D. 45 2014 The Strauss conjecture on Kerr black hole backgrounds. Zbl 1295.35327Lindblad, Hans; Metcalfe, Jason; Sogge, Christopher D.; Tohaneanu, Mihai; Wang, Chengbo 28 2014 On eigenfunction restriction estimates and \(L^4\)-bounds for compact surfaces with nonpositive curvature. Zbl 1307.58013Sogge, Christopher D.; Zelditch, Steve 15 2014 A few endpoint geodesic restriction estimates for eigenfunctions. Zbl 1293.58011Chen, Xuehua; Sogge, Christopher D. 14 2014 Concerning \(L^p\) resolvent estimates for simply connected manifolds of constant curvature. Zbl 1303.53052Huang, Shanlin; Sogge, Christopher D. 9 2014 Remarks on global solutions for nonlinear wave equations under the standard null conditions. Zbl 1262.35170Lindblad, Hans; Nakamura, Makoto; Sogge, Christopher D. 11 2013 Strichartz estimates for Dirichlet-wave equations in two dimensions with applications. Zbl 1246.35052Smith, Hart F.; Sogge, Christopher D.; Wang, Chengbo 23 2012 A natural lower bound for the size of nodal sets. Zbl 1329.35224Hezari, Hamid; Sogge, Christopher D. 19 2012 Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary. Zbl 1262.58015Blair, Matthew D.; Smith, Hart F.; Sogge, Chris D. 19 2012 Lower bounds on the Hausdorff measure of nodal sets. II. Zbl 1283.58020Sogge, Christopher D.; Zelditch, Steve 17 2012 Concerning the \(L^4\) norms of typical eigenfunctions on compact surfaces. Zbl 1317.58035Sogge, Christopher D.; Zelditch, Steve 7 2012 Lower bounds on the Hausdorff measure of nodal sets. Zbl 1242.58017Sogge, Christopher D.; Zelditch, Steve 29 2011 Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions. Zbl 1234.35156Sogge, Christopher D. 24 2011 About the blowup of quasimodes on Riemannian manifolds. Zbl 1214.58012Sogge, Christopher D.; Toth, John A.; Zelditch, Steve 23 2011 On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles. Zbl 1193.35100Hidano, Kunio; Metcalfe, Jason; Smith, Hart F.; Sogge, Christopher D.; Zhou, Yi 37 2010 Concerning the wave equation on asymptotically Euclidean manifolds. Zbl 1231.35030Sogge, Christopher D.; Wang, Chengbo 21 2010 Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Zbl 1213.35314Metcalfe, Jason; Sogge, Christopher D. 11 2010 Strichartz estimates for the wave equation on manifolds with boundary. Zbl 1198.58012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 44 2009 Lectures on nonlinear wave equations. 2nd ed. Zbl 1165.35001Sogge, Christopher D. 52 2008 On Strichartz estimates for Schrödinger operators in compact manifolds with boundary. Zbl 1169.35012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 25 2008 Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Zbl 1209.35083Du, Yi; Metcalfe, Jason; Sogge, Christopher D.; Zhou, Yi 23 2008 Fourier integrals in classical analysis. Paperback reprint of the hardback edition 1993. Zbl 1143.35002Sogge, Christopher D. 4 2008 On multilinear spectral cluster estimates for manifolds with boundary. Zbl 1146.58019Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 3 2008 Lectures on eigenfunctions of the Laplacian. Zbl 1170.35071Sogge, Christopher D. 1 2008 On the \(L^p\) norm of spectral clusters for compact manifolds with boundary. Zbl 1189.58017Smith, Hart F.; Sogge, Christopher D. 37 2007 Global existence of null-form wave equations in exterior domains. Zbl 1138.35065Metcalfe, Jason; Sogge, Christopher D. 34 2007 Long-time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods. Zbl 1162.35052Metcalfe, Jason; Sogge, Christopher D. 46 2006 Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions. Zbl 1185.35140Metcalfe, Jason; Sogge, Christopher D. 13 2006 Hyperbolic trapped rays and global existence of quasilinear wave equations. Zbl 1077.35083Metcalfe, Jason; Sogge, Christopher D. 26 2005 Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains. Zbl 1149.35055Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 15 2005 Nonlinear hyperbolic equations in infinite homogeneous waveguides. Zbl 1078.35076Metcalfe, Jason; Sogge, Christopher D.; Stewart, Ann Ann 13 2005 Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition. Zbl 1098.35112Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 53 2004 Global existence for nonlinear wave equations with multiple speeds. Zbl 1052.35133Sogge, Christopher D. 16 2003 Almost global existence for some semilinear wave equations. Zbl 1031.35107Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 55 2002 Riemannian manifolds with maximal eigenfunction growth. Zbl 1018.58010Sogge, Christopher D.; Zelditch, Steve 44 2002 Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 29 2002 Eigenfunction and Bochner Riesz estimates on manifolds with boundary. Zbl 1017.58016Sogge, Christopher D. 18 2002 Global Strichartz estimates for nontrapping perturbations of the Laplacian. Zbl 0972.35014Smith, Hart F.; Sogge, Christopher D. 91 2000 On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 5 2000 Null form estimates for \((1/2,1/2)\) symbols and local existence for a quasilinear Dirichlet-wave equation. Zbl 1016.35008Smith, Hart F.; Sogge, Christopher D. 2 2000 Concerning Nikodym-type sets in 3-dimensional curved spaces. Zbl 0968.42016Sogge, Christopher D. 9 1999 Averages over curves with torsion. Zbl 0934.42008Oberlin, Daniel; Smith, Hart F.; Sogge, Christopher D. 4 1998 Weighted Strichartz estimates and global existence for semilinear wave equations. Zbl 0893.35075Georgiev, Vladimir; Lindblad, Hans; Sogge, Christopher D. 126 1997 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 25 1997 Negative results for Nikodym maximal functions and related oscillatory integrals in curved space. Zbl 0884.42016Minicozzi, William P. II; Sogge, Christopher D. 15 1997 Long-time existence for small amplitude semilinear wave equations. Zbl 0869.35064Lindblad, Hans; Sogge, Christopher D. 70 1996 Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions. Zbl 0865.35077Lindblad, Hans; Sogge, Christopher D. 6 1996 On existence and scattering with minimal regularity for semilinear wave equations. Zbl 0846.35085Lindblad, Hans; Sogge, Christopher D. 179 1995 Lectures on nonlinear wave equations. Zbl 1089.35500Sogge, Christopher D. 84 1995 On the critical semilinear wave equation outside convex obstacles. Zbl 0860.35081Smith, Hart F.; Sogge, Christopher D. 36 1995 Maximal operators associated to hypersurfaces with one nonvanishing principal curvature. Zbl 0880.42011Sogge, Christopher D. 15 1995 Smoothing estimates for the wave equation and applications. Zbl 0901.35050Sogge, Christopher D. 2 1995 On Strichartz and eigenfunction estimates for low regularity metrics. Zbl 0832.35018Smith, Hart F.; Sogge, Christopher D. 13 1994 \(L^ p\) regularity for the wave equation with strictly convex obstacles. Zbl 0805.35169Smith, Hart F.; Sogge, Christopher D. 6 1994 Fourier integrals in classical analysis. Zbl 0783.35001Sogge, Christopher D. 202 1993 Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. Zbl 0776.58037Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 76 1993 On local existence for nonlinear wave equations satisfying variable coefficient null conditions. Zbl 0792.35125Sogge, Christopher D. 4 1993 \(L^ p\) estimates for the wave equation and applications. Zbl 0796.35111Sogge, Christopher D. 3 1993 Wave front sets, local smoothing and Bourgain’s circular maximal theorem. Zbl 0759.42016Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 57 1992 Uniqueness in Cauchy problems for hyperbolic differential operators. Zbl 0763.35012Sogge, Christopher D. 6 1992 Sobolev estimates for the wave operator on compact manifolds. Zbl 0799.35157Jerison, D.; Sogge, C. D.; Zhou, Z. 1 1992 Decay estimates for Schrödinger operators. Zbl 0743.35008Journé, J.-L.; Soffer, A.; Sogge, C. D. 117 1991 Regularity properties of Fourier integral operators. Zbl 0754.58037Seeger, Andreas; Sogge, Christopher D.; Stein, Elias M. 99 1991 Propagation of singularities and maximal functions in the plane. Zbl 0754.35004Sogge, Christopher D. 43 1991 Strong uniqueness theorems for second order elliptic differential equations. Zbl 0734.35012Sogge, Christopher D. 29 1990 A unique continuation theorem for second order parabolic differential operators. Zbl 0704.35016Sogge, C. D. 21 1990 Averages over hypersurfaces. Smoothness of generalized Radon transforms. Zbl 0695.42012Sogge, C. D.; Stein, Elias M. 17 1990 Oscillatory integrals associated to folding canonical relations. Zbl 0746.58076Pan, Yibiao; Sogge, Christopher D. 15 1990 \(L^ p \to{} L^{p'}\) estimates for time-dependent Schrödinger operators. Zbl 0751.35011Journé, J. L.; Soffer, A.; Sogge, C. D. 3 1990 On the boundedness of functions of (pseudo-) differential operators on compact manifolds. Zbl 0698.35169Seeger, A.; Sogge, C. D. 41 1989 Bounds for eigenfunctions of differential operators. Zbl 0703.35133Seeger, A.; Sogge, C. D. 28 1989 Oscillatory integrals and unique continuation for second order elliptic differential equations. Zbl 0703.35027Sogge, Christopher D. 14 1989 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,298 Authors 62 Sogge, Christopher D. 27 Wang, Chengbo 25 Seeger, Andreas 24 Lee, Sanghyuk 22 Metcalfe, Jason L. 17 Burq, Nicolas 17 Kenig, Carlos Eduardo 17 Smith, Hart F. 16 Tzvetkov, Nikolay 16 Zhang, Junyong 16 Zhou, Yi 15 Cuccagna, Scipio 15 Hidano, Kunio 15 Ruzhansky, Michael V. 15 Tataru, Daniel 14 Iosevich, Alex 14 Schlag, Wilhelm 14 Seo, Ihyeok 13 Blair, Matthew D. 13 D’Ancona, Piero 13 Goldberg, Michael Joseph 13 Lai, Ningan 13 Merle, Frank 13 Soffer, Avraham 12 Green, William R. 12 Planchon, Fabrice 12 Toth, John Andrew 12 Yao, Xiaohua 12 Zha, Dongbing 12 Zheng, Jiqiang 11 Fan, Dashan 11 Han, Wei 11 Müller, Detlef 11 Vega, Luis 11 Yin, Huicheng 11 Zelditch, Steve 10 Fang, Daoyuan 10 Miao, Changxing 10 Mizutani, Haruya 10 Oh, Tadahiro 10 Tao, Terence 10 Tohaneanu, Mihai 10 Witt, Ingo 9 Duyckaerts, Thomas 9 Erdoğan, Mehmet Burak 9 Hassell, Andrew 9 Kubo, Hideo 9 Manna, Ramesh 9 Palmieri, Alessandro 9 Staubach, Wolfgang 9 Wakasa, Kyouhei 9 Zaag, Hatem 9 Zhu, Jiuyi 8 Cuenin, Jean-Claude 8 D’Abbicco, Marcello 8 Dodson, Benjamin G. 8 Galkowski, Jeffrey 8 Gerard, Patrick 8 Germain, Pierre 8 Hickman, Jonathan 8 Ivanovici, Oana 8 Kharibegashvili, S. S. 8 Lawrie, Andrew G. W. 8 Sikora, Adam S. 8 Stein, Elias Menachem 8 Sugimoto, Mitsuru 8 Tacy, Melissa 8 Takamura, Hiroyuki 8 Yan, Lixin 8 Zhang, Cheng 7 Beltran, David 7 Casarino, Valentina 7 Dong, Shijie 7 Donninger, Roland 7 Evéquoz, Gilles 7 Greenblatt, Michael 7 Huang, Xiaoqi 7 Jleli, Mohamed Boussairi 7 Katayama, Soichiro 7 Klainerman, Sergiu 7 Koch, Herbert 7 Kwon, Yehyun 7 Lebeau, Gilles 7 Lindblad, Hans 7 Marzuola, Jeremy Louis 7 Ratnakumar, P. K. 7 Samet, Bessem 7 Xi, Yakun 6 Canzani, Yaiza 6 Chen, Jiecheng 6 Chen, Peng 6 Ciatti, Paolo 6 Ebert, Marcelo Rempel 6 Escauriaza Zubiria, Luis 6 Frank, Rupert L. 6 Han, Xiaolong 6 Hong, Sunggeum 6 Ikromov, Isroil A. 6 Mandel, Rainer 6 Martini, Alessio ...and 1,198 more Authors all top 5 Cited in 245 Serials 100 Journal of Functional Analysis 90 Journal of Differential Equations 80 Communications in Partial Differential Equations 73 Journal of Mathematical Analysis and Applications 71 Communications in Mathematical Physics 68 Transactions of the American Mathematical Society 50 Proceedings of the American Mathematical Society 48 Nonlinear Analysis. Theory, Methods & Applications. 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Académie des Sciences, Paris 12 Journal of Hyperbolic Differential Equations 11 Geometric and Functional Analysis. GAFA 10 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Chinese Annals of Mathematics. Series B 9 Calculus of Variations and Partial Differential Equations 8 Applied and Computational Harmonic Analysis 7 Mathematische Nachrichten 7 Bulletin of the American Mathematical Society. New Series 7 Analysis and Mathematical Physics 6 Arkiv för Matematik 6 Reviews in Mathematical Physics 6 Acta Mathematica 6 Illinois Journal of Mathematics 6 Journal of the Mathematical Society of Japan 6 Tôhoku Mathematical Journal. Second Series 6 Applied Mathematics Letters 6 Selecta Mathematica. New Series 6 Annals of Mathematics. Second Series 6 Acta Mathematica Sinica. English Series 6 Communications in Contemporary Mathematics 6 Stochastic and Partial Differential Equations. Analysis and Computations 5 Letters in Mathematical Physics 5 Mathematical Methods in the Applied Sciences 5 Mathematical Notes 5 Nonlinearity 5 Integral Equations and Operator Theory 5 Annals of PDE 5 Pure and Applied Analysis 4 Applicable Analysis 4 Israel Journal of Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Monatshefte für Mathematik 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Bulletin des Sciences Mathématiques 4 Differential Equations 4 Journal of the Institute of Mathematics of Jussieu 4 Science China. Mathematics 4 Journal of Pseudo-Differential Operators and Applications 4 Bulletin of Mathematical Sciences 4 Forum of Mathematics, Sigma 4 Journal de l’École Polytechnique – Mathématiques 3 Inverse Problems 3 Mathematics of Computation 3 Applied Mathematics and Computation 3 Applied Mathematics and Optimization 3 Archiv der Mathematik 3 Functional Analysis and its Applications 3 Indiana University Mathematics Journal 3 Journal of the London Mathematical Society. Second Series 3 Journal für die Reine und Angewandte Mathematik 3 Manuscripta Mathematica 3 Memoirs of the American Mathematical Society 3 Pacific Journal of Mathematics 3 Quarterly of Applied Mathematics 3 Results in Mathematics 3 Annals of Global Analysis and Geometry 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 NoDEA. Nonlinear Differential Equations and Applications 3 Nonlinear Analysis. Real World Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Mediterranean Journal of Mathematics 3 Journal of Spectral Theory 3 Séminaire Laurent Schwartz. EDP et Applications 3 Tunisian Journal of Mathematics 2 Classical and Quantum Gravity 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Russian Mathematical Surveys ...and 145 more Serials all top 5 Cited in 53 Fields 1,219 Partial differential equations (35-XX) 392 Harmonic analysis on Euclidean spaces (42-XX) 253 Global analysis, analysis on manifolds (58-XX) 148 Operator theory (47-XX) 109 Quantum theory (81-XX) 65 Functional analysis (46-XX) 58 Differential geometry (53-XX) 51 Abstract harmonic analysis (43-XX) 47 Number theory (11-XX) 47 Dynamical systems and ergodic theory (37-XX) 47 Fluid mechanics (76-XX) 35 Relativity and gravitational theory (83-XX) 34 Probability theory and stochastic processes (60-XX) 29 Topological groups, Lie groups (22-XX) 28 Integral transforms, operational calculus (44-XX) 25 Special functions (33-XX) 24 Mechanics of deformable solids (74-XX) 22 Measure and integration (28-XX) 21 Systems theory; control (93-XX) 20 Numerical analysis (65-XX) 18 Optics, electromagnetic theory (78-XX) 14 Ordinary differential equations (34-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Functions of a complex variable (30-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Approximations and expansions (41-XX) 10 Real functions (26-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Integral equations (45-XX) 8 Mechanics of particles and systems (70-XX) 7 Potential theory (31-XX) 6 Combinatorics (05-XX) 5 General and overarching topics; collections (00-XX) 5 Algebraic geometry (14-XX) 5 Computer science (68-XX) 4 Difference and functional equations (39-XX) 4 Convex and discrete geometry (52-XX) 4 Geophysics (86-XX) 4 Information and communication theory, circuits (94-XX) 3 Geometry (51-XX) 3 Statistics (62-XX) 3 Astronomy and astrophysics (85-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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