Edit Profile (opens in new tab) Croke, Christopher B. Co-Author Distance Author ID: croke.christopher-b Published as: Croke, Christopher B.; Croke, Christopher; Croke, C.; Croke, C. B. more...less Documents Indexed: 50 Publications since 1980, including 2 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 21 Co-Authors with 26 Joint Publications 728 Co-Co-Authors all top 5 Co-Authors 25 single-authored 8 Kleiner, Bruce 4 Katz, Mikhail G. 3 Dairbekov, Nurlan Slyamkhanovich 3 Sharafutdinov, Vladimir A. 2 Bangert, Victor 2 Fathi, Albert 2 Ivanov, Sergei Vladimirovich 2 Wen, Haomin 1 Balacheff, Florent 1 Chambers, Gregory R. 1 Derdzinski, Andrzej 1 Eberlein, Patrick B. 1 Feldman, Jacob 1 Herreros, Pilar 1 Karcher, Hermann 1 Lasiecka, Irena 1 Liokumovich, Yevgeny 1 Schröder, Viktor M. H. 1 Uhlmann, Gunther Alberto 1 Vogelius, Michael S. 1 Weinstein, Alan David all top 5 Serials 6 Journal of Differential Geometry 6 Proceedings of the American Mathematical Society 5 Inventiones Mathematicae 4 Commentarii Mathematici Helvetici 4 Topology 4 Ergodic Theory and Dynamical Systems 3 Duke Mathematical Journal 3 Transactions of the American Mathematical Society 3 Geometric and Functional Analysis. GAFA 2 Bulletin of the London Mathematical Society 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Pacific Journal of Mathematics 1 International Journal of Mathematics 1 Communications in Analysis and Geometry 1 Doklady Mathematics 1 The Asian Journal of Mathematics 1 The IMA Volumes in Mathematics and its Applications all top 5 Fields 48 Differential geometry (53-XX) 4 Convex and discrete geometry (52-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Partial differential equations (35-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Mechanics of particles and systems (70-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 45 Publications have been cited 841 times in 596 Documents Cited by ▼ Year ▼ Some isoperimetric inequalities and eigenvalue estimates. Zbl 0465.53032 Croke, Christopher B. 133 1980 Rigidity for surfaces of non-positive curvature. Zbl 0704.53035 Croke, Christopher B. 89 1990 Spaces with nonpositive curvature and their ideal boundaries. Zbl 0959.53014 Croke, Christopher B.; Kleiner, Bruce 60 2000 Rigidity and the distance between boundary points. Zbl 0729.53043 Croke, Christopher B. 53 1991 Area and the length of the shortest closed geodesic. Zbl 0642.53045 Croke, Christopher B. 43 1988 Spectral rigidity of a compact negatively curved manifold. Zbl 0936.58013 Croke, Christopher B.; Sharafutdinov, Vladimir A. 42 1998 A sharp four dimensional isoperimetric inequality. Zbl 0552.53017 Croke, Christopher B. 38 1984 The marked length-spectrum of a surface of nonpositive curvature. Zbl 0779.53025 Croke, C.; Fathi, A.; Feldman, J. 28 1992 Local boundary rigidity of a compact Riemannian manifold with curvature bounded above. Zbl 0958.53027 Croke, Christopher B.; Dairbekov, Nurlan S.; Sharafutdinov, Vladimir A. 25 2000 Universal volume bounds in Riemannian manifolds. Zbl 1051.53026 Croke, Christopher B.; Katz, Mikhail 23 2003 Rigidity theorems in Riemannian geometry. Zbl 1080.53033 Croke, Christopher B. 23 2003 Conjugacy and rigidity for manifolds with a parallel vector field. Zbl 0807.53035 Croke, Christopher B.; Kleiner, Bruce 21 1994 The geodesic flow of a nonpositively curved graph manifold. Zbl 1035.53116 Croke, C. B.; Kleiner, B. 20 2002 An eigenvalue pinching theorem. Zbl 0505.53018 Croke, Christopher B. 20 1982 The fundamental group of compact manifolds without conjugate points. Zbl 0608.53038 Croke, Christopher B.; Schroeder, Viktor 19 1986 Volumes of small balls on open manifolds: Lower bounds and examples. Zbl 0709.53033 Croke, Christopher B.; Karcher, Hermann 17 1988 An inequality between energy and intersection. Zbl 0719.53020 Croke, C.; Fathi, A. 14 1990 Boundary case of equality in optimal Loewner-type inequalities. Zbl 1122.53020 Bangert, Victor; Croke, Christopher; Ivanov, Sergei V.; Katz, Mikhail G. 13 2007 The first eigenvalue of the Laplacian for plane domains. Zbl 0462.35071 Croke, Christopher B. 12 1981 A Zoll counterexample to a geodesic length conjecture. Zbl 1201.53050 Balacheff, Florent; Croke, Christopher; Katz, Mikhail G. 12 2009 Closed curves on convex hypersurfaces and periods of nonlinear oscillations. Zbl 0471.70020 Croke, Christopher B.; Weinstein, Alan 11 1981 Filling area conjecture and ovalless real hyperelliptic surfaces. Zbl 1082.53033 Bangert, V.; Croke, C.; Ivanov, S.; Katz, M. 11 2005 A warped product splitting theorem. Zbl 0772.53030 Croke, Christopher B.; Kleiner, Bruce 11 1992 Lengths and volumes in Riemannian manifolds. Zbl 1073.53053 Croke, Christopher B.; Dairbekov, Nurlan S. 10 2004 Volumes of balls in manifolds without conjugate points. Zbl 0772.53031 Croke, Christopher B. 10 1992 Scattering rigidity with trapped geodesics. Zbl 1296.53083 Croke, Christopher 9 2014 On tori without conjugate points. Zbl 0842.53028 Croke, Christopher B.; Kleiner, Bruce 9 1995 Poincaré’s problem and the length of the shortest closed geodesic on a convex hypersurface. Zbl 0501.53031 Croke, Christopher B. 9 1982 A rigidity theorem for simply connected manifolds without conjugate points. Zbl 0924.53027 Croke, Christopher B.; Kleiner, Bruce 7 1998 Curvature free volume estimates. Zbl 0552.53016 Croke, Christopher B. 7 1984 Boundary and lens rigidity of finite quotients. Zbl 1081.53037 Croke, Christopher 6 2005 Lens rigidity with trapped geodesics in two dimensions. Zbl 1339.53038 Croke, Christopher B.; Herreros, Pilar 6 2016 Conjugacy and rigidity for nonpositively curved manifolds of higher rank. Zbl 0859.53024 Croke, Christopher B.; Eberlein, Patrick; Kleiner, Bruce 4 1996 A synthetic characterization of the hemisphere. Zbl 1136.53037 Croke, Christopher B. 4 2008 Simply connected manifolds with no conjugate points which are flat outside a compact set. Zbl 0718.53030 Croke, Christopher B. 3 1991 Lower bounds on the energy of maps. Zbl 0634.53042 Croke, Christopher B. 3 1987 On the volume of metric balls. Zbl 0521.53044 Croke, Christopher B. 3 1983 A rigidity theorem for manifolds without conjugate points. Zbl 0924.53028 Croke, Christopher B.; Kleiner, Bruce 2 1998 The volume and lengths on a three sphere. Zbl 1029.53041 Croke, Christopher B. 2 2002 A lower bound for \(\lambda _ 1\) on manifolds with boundary. Zbl 0617.53047 Croke, Christopher B.; Derdziński, Andrzej 2 1987 An isoembolic pinching theorem. Zbl 0648.53025 Croke, Christopher B. 2 1988 Riemannian manifolds with large invariants. Zbl 0497.53047 Croke, Christopher B. 2 1980 Conjugacy rigidity for non-positively curved graph manifolds. Zbl 1062.53032 Croke, Christopher B. 1 2004 Geometric methods in inverse problems and PDE control. Selected articles presented at the 2001 IMA summer program, Minneapolis, MN, USA. Zbl 1051.35003 1 2003 Area of small disks. Zbl 1177.53041 Croke, Christopher B. 1 2009 Lens rigidity with trapped geodesics in two dimensions. Zbl 1339.53038 Croke, Christopher B.; Herreros, Pilar 6 2016 Scattering rigidity with trapped geodesics. Zbl 1296.53083 Croke, Christopher 9 2014 A Zoll counterexample to a geodesic length conjecture. Zbl 1201.53050 Balacheff, Florent; Croke, Christopher; Katz, Mikhail G. 12 2009 Area of small disks. Zbl 1177.53041 Croke, Christopher B. 1 2009 A synthetic characterization of the hemisphere. Zbl 1136.53037 Croke, Christopher B. 4 2008 Boundary case of equality in optimal Loewner-type inequalities. Zbl 1122.53020 Bangert, Victor; Croke, Christopher; Ivanov, Sergei V.; Katz, Mikhail G. 13 2007 Filling area conjecture and ovalless real hyperelliptic surfaces. Zbl 1082.53033 Bangert, V.; Croke, C.; Ivanov, S.; Katz, M. 11 2005 Boundary and lens rigidity of finite quotients. Zbl 1081.53037 Croke, Christopher 6 2005 Lengths and volumes in Riemannian manifolds. Zbl 1073.53053 Croke, Christopher B.; Dairbekov, Nurlan S. 10 2004 Conjugacy rigidity for non-positively curved graph manifolds. Zbl 1062.53032 Croke, Christopher B. 1 2004 Universal volume bounds in Riemannian manifolds. Zbl 1051.53026 Croke, Christopher B.; Katz, Mikhail 23 2003 Rigidity theorems in Riemannian geometry. Zbl 1080.53033 Croke, Christopher B. 23 2003 Geometric methods in inverse problems and PDE control. Selected articles presented at the 2001 IMA summer program, Minneapolis, MN, USA. Zbl 1051.35003 1 2003 The geodesic flow of a nonpositively curved graph manifold. Zbl 1035.53116 Croke, C. B.; Kleiner, B. 20 2002 The volume and lengths on a three sphere. Zbl 1029.53041 Croke, Christopher B. 2 2002 Spaces with nonpositive curvature and their ideal boundaries. Zbl 0959.53014 Croke, Christopher B.; Kleiner, Bruce 60 2000 Local boundary rigidity of a compact Riemannian manifold with curvature bounded above. Zbl 0958.53027 Croke, Christopher B.; Dairbekov, Nurlan S.; Sharafutdinov, Vladimir A. 25 2000 Spectral rigidity of a compact negatively curved manifold. Zbl 0936.58013 Croke, Christopher B.; Sharafutdinov, Vladimir A. 42 1998 A rigidity theorem for simply connected manifolds without conjugate points. Zbl 0924.53027 Croke, Christopher B.; Kleiner, Bruce 7 1998 A rigidity theorem for manifolds without conjugate points. Zbl 0924.53028 Croke, Christopher B.; Kleiner, Bruce 2 1998 Conjugacy and rigidity for nonpositively curved manifolds of higher rank. Zbl 0859.53024 Croke, Christopher B.; Eberlein, Patrick; Kleiner, Bruce 4 1996 On tori without conjugate points. Zbl 0842.53028 Croke, Christopher B.; Kleiner, Bruce 9 1995 Conjugacy and rigidity for manifolds with a parallel vector field. Zbl 0807.53035 Croke, Christopher B.; Kleiner, Bruce 21 1994 The marked length-spectrum of a surface of nonpositive curvature. Zbl 0779.53025 Croke, C.; Fathi, A.; Feldman, J. 28 1992 A warped product splitting theorem. Zbl 0772.53030 Croke, Christopher B.; Kleiner, Bruce 11 1992 Volumes of balls in manifolds without conjugate points. Zbl 0772.53031 Croke, Christopher B. 10 1992 Rigidity and the distance between boundary points. Zbl 0729.53043 Croke, Christopher B. 53 1991 Simply connected manifolds with no conjugate points which are flat outside a compact set. Zbl 0718.53030 Croke, Christopher B. 3 1991 Rigidity for surfaces of non-positive curvature. Zbl 0704.53035 Croke, Christopher B. 89 1990 An inequality between energy and intersection. Zbl 0719.53020 Croke, C.; Fathi, A. 14 1990 Area and the length of the shortest closed geodesic. Zbl 0642.53045 Croke, Christopher B. 43 1988 Volumes of small balls on open manifolds: Lower bounds and examples. Zbl 0709.53033 Croke, Christopher B.; Karcher, Hermann 17 1988 An isoembolic pinching theorem. Zbl 0648.53025 Croke, Christopher B. 2 1988 Lower bounds on the energy of maps. Zbl 0634.53042 Croke, Christopher B. 3 1987 A lower bound for \(\lambda _ 1\) on manifolds with boundary. Zbl 0617.53047 Croke, Christopher B.; Derdziński, Andrzej 2 1987 The fundamental group of compact manifolds without conjugate points. Zbl 0608.53038 Croke, Christopher B.; Schroeder, Viktor 19 1986 A sharp four dimensional isoperimetric inequality. Zbl 0552.53017 Croke, Christopher B. 38 1984 Curvature free volume estimates. Zbl 0552.53016 Croke, Christopher B. 7 1984 On the volume of metric balls. Zbl 0521.53044 Croke, Christopher B. 3 1983 An eigenvalue pinching theorem. Zbl 0505.53018 Croke, Christopher B. 20 1982 Poincaré’s problem and the length of the shortest closed geodesic on a convex hypersurface. Zbl 0501.53031 Croke, Christopher B. 9 1982 The first eigenvalue of the Laplacian for plane domains. Zbl 0462.35071 Croke, Christopher B. 12 1981 Closed curves on convex hypersurfaces and periods of nonlinear oscillations. Zbl 0471.70020 Croke, Christopher B.; Weinstein, Alan 11 1981 Some isoperimetric inequalities and eigenvalue estimates. Zbl 0465.53032 Croke, Christopher B. 133 1980 Riemannian manifolds with large invariants. Zbl 0497.53047 Croke, Christopher B. 2 1980 all cited Publications top 5 cited Publications all top 5 Cited by 662 Authors 17 Uhlmann, Gunther Alberto 15 Croke, Christopher B. 13 Rotman, Regina 11 Katz, Mikhail G. 11 Stefanov, Plamen D. 10 Lefeuvre, Thibault 9 Ivanov, Sergei Vladimirovich 9 Nabutovsky, Alexander 8 Ilmavirta, Joonas 8 Sabourau, Stéphane 7 Guillarmou, Colin 7 Paternain, Gabriel Pedro 6 Anderson, Michael T. 6 Dairbekov, Nurlan Slyamkhanovich 6 Kaloshin, Vadim Yu. 6 Kleiner, Bruce 6 Ruggiero, Rafael Oswaldo 6 Tian, Gang 5 Abbondandolo, Alberto 5 Adelstein, Ian M. 5 Charney, Ruth Michele 5 Colbois, Bruno 5 de Hoop, Maarten V. 5 Gallot, Sylvestre 5 Kristály, Alexandru 5 Lassas, Matti J. 5 Mooney, Christopher P. 5 Paeng, Seong-Hun 5 Saksala, Teemu 5 Vasy, András 5 Zhou, Hanming 4 Balacheff, Florent 4 Besson, Gérard 4 Burago, Dmitri 4 Chen, Xiuxiong 4 Courtois, Gilles 4 Dibble, James 4 Gordon, Carolyn S. 4 Guilbault, Craig R. 4 Hamenstädt, Ursula 4 Hosaka, Tetsuya 4 Kim, Changwan 4 Lafont, Jean-François 4 Leininger, Christopher J. 4 Mazzucchelli, Marco 4 Qing, Yulan 4 Rachele, Lizabeth V. 4 Schröder, Viktor M. H. 4 Wang, Feng-Yu 3 Bangert, Victor 3 Bialy, Misha 3 Bonthonneau, Yannick Guedes 3 Bramham, Barney 3 Constantine, David 3 de Simoi, Jacopo 3 Fanaï, Hamid-Reza 3 Fogagnolo, Mattia 3 Gornet, Ruth 3 Hagen, Mark F. 3 Hebey, Emmanuel 3 Hruska, G. Christopher 3 Hryniewicz, Umberto L. 3 Huang, Jingyin 3 Kasue, Atsushi 3 Kim, Inkang 3 Kuwae, Kazuhiro 3 Liokumovich, Yevgeny 3 Ma, Shiguang 3 Meda, Stefano 3 Murray, Devin 3 Papasoglu, Panos 3 Qing, Jie 3 Rosenberg, Steven 3 Sakurai, Yohei 3 Salo, Mikko 3 Salomão, Pedro Antonio Santoro 3 Swenson, Eric L. 2 Abreu, Miguel 2 Álvarez Paiva, Juan Carlos 2 Antonelli, Gioacchino 2 Avinyo, Albert 2 Bando, Shigetoshi 2 Benjamini, Itai 2 Bérard, Pierre H. 2 Beyrer, Jonas 2 Brasco, Lorenzo 2 Buyalo, Sergei V. 2 Cao, ChunJun 2 Cao, Jianguo 2 Caprace, Pierre-Emmanuel 2 Cashen, Christopher H. 2 Cavalletti, Fabio 2 Chang, Shu-Cheng 2 Chavel, Isaac 2 Choe, Jaigyoung 2 Colding, Tobias Holck 2 Collins, Tristan Clifford 2 Cordes, Matthew 2 Creutz, Paul 2 Duchin, Moon ...and 562 more Authors all top 5 Cited in 153 Serials 34 The Journal of Geometric Analysis 30 Geometriae Dedicata 29 Proceedings of the American Mathematical Society 25 Inventiones Mathematicae 23 Transactions of the American Mathematical Society 19 Mathematische Zeitschrift 18 Duke Mathematical Journal 18 Mathematische Annalen 16 Geometric and Functional Analysis. GAFA 15 Geometry & Topology 14 Israel Journal of Mathematics 14 Advances in Mathematics 14 Ergodic Theory and Dynamical Systems 11 Annales de l’Institut Fourier 10 Journal of Functional Analysis 10 Calculus of Variations and Partial Differential Equations 9 Communications in Mathematical Physics 9 Differential Geometry and its Applications 7 Inverse Problems and Imaging 7 Journal of Topology and Analysis 6 Compositio Mathematica 6 Journal of the American Mathematical Society 6 Communications in Contemporary Mathematics 6 Algebraic & Geometric Topology 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Commentarii Mathematici Helvetici 5 Journal für die Reine und Angewandte Mathematik 5 Manuscripta Mathematica 5 Revista Matemática Iberoamericana 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Annals of Mathematics. Second Series 5 Groups, Geometry, and Dynamics 4 Bulletin of the London Mathematical Society 4 Journal of Differential Equations 4 Journal of Differential Geometry 4 Nagoya Mathematical Journal 4 St. Petersburg Mathematical Journal 4 Journal of Fixed Point Theory and Applications 4 Journal of Topology 4 Science China. Mathematics 3 Archive for Rational Mechanics and Analysis 3 Bulletin de la Société Mathématique de France 3 Pacific Journal of Mathematics 3 Tôhoku Mathematical Journal. Second Series 3 Annals of Global Analysis and Geometry 3 Communications in Partial Differential Equations 3 Expositiones Mathematicae 3 Discrete and Continuous Dynamical Systems 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Oberwolfach Reports 3 Analysis & PDE 2 Journal d’Analyse Mathématique 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Rocky Mountain Journal of Mathematics 2 Journal of Geometry and Physics 2 Acta Mathematica 2 Indiana University Mathematics Journal 2 Journal of the London Mathematical Society. Second Series 2 Michigan Mathematical Journal 2 Topology and its Applications 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 International Journal of Algebra and Computation 2 Bulletin of the American Mathematical Society. New Series 2 Potential Analysis 2 Journal of Mathematical Sciences (New York) 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Journal of High Energy Physics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Bulletin of the Brazilian Mathematical Society. New Series 2 International Journal of Geometric Methods in Modern Physics 2 Forum of Mathematics, Sigma 2 Journal de l’École Polytechnique – Mathématiques 2 Annales Henri Lebesgue 1 Bulletin of the Australian Mathematical Society 1 Classical and Quantum Gravity 1 Communications on Pure and Applied Mathematics 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Nonlinearity 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 ACM Transactions on Mathematical Software 1 American Journal of Mathematics 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Czechoslovak Mathematical Journal 1 Publications Mathématiques 1 International Journal for Numerical Methods in Engineering 1 Journal of Combinatorial Theory. Series B 1 Journal of the Mathematical Society of Japan 1 Journal of Pure and Applied Algebra 1 Kodai Mathematical Journal 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik ...and 53 more Serials all top 5 Cited in 52 Fields 430 Differential geometry (53-XX) 146 Global analysis, analysis on manifolds (58-XX) 85 Dynamical systems and ergodic theory (37-XX) 83 Manifolds and cell complexes (57-XX) 79 Group theory and generalizations (20-XX) 65 Partial differential equations (35-XX) 26 Several complex variables and analytic spaces (32-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 19 Functions of a complex variable (30-XX) 19 Convex and discrete geometry (52-XX) 16 Geometry (51-XX) 14 Probability theory and stochastic processes (60-XX) 13 Integral transforms, operational calculus (44-XX) 13 Functional analysis (46-XX) 12 Potential theory (31-XX) 9 Topological groups, Lie groups (22-XX) 9 Operator theory (47-XX) 8 Algebraic topology (55-XX) 7 Algebraic geometry (14-XX) 7 Measure and integration (28-XX) 7 Relativity and gravitational theory (83-XX) 6 General topology (54-XX) 6 Mechanics of particles and systems (70-XX) 6 Quantum theory (81-XX) 5 General and overarching topics; collections (00-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Numerical analysis (65-XX) 5 Geophysics (86-XX) 4 Combinatorics (05-XX) 4 Real functions (26-XX) 4 Mechanics of deformable solids (74-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Ordinary differential equations (34-XX) 3 Information and communication theory, circuits (94-XX) 2 Abstract harmonic analysis (43-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Citations by Year