Arkhipova, N. A.; Stepanov, S. E. Two kernel vanishing theorems and an estimation theorem for the smallest eigenvalue of the Hodge-de Rham Laplacian. (English) Zbl 07947719 Differ. Geom. Mnogoobr. Figur 55, No. 2, 37-46 (2024). MSC: 53C21 58J50 × Cite Format Result Cite Review PDF Full Text: DOI
Ganatra, Sheel Cyclic homology, \(S^1\)-equivariant Floer cohomology and Calabi-Yau structures. (English) Zbl 1545.53079 Geom. Topol. 27, No. 9, 3461-3584 (2023). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 53D37 14J32 14J33 19D55 18G90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Colbois, Bruno; El Soufi, Ahmad; Ilias, Saïd; Savo, Alessandro Eigenvalues upper bounds for the magnetic Schrödinger operator. (English) Zbl 1518.58005 Commun. Anal. Geom. 30, No. 4, 779-814 (2022). Reviewer: Martin Chuaqui Farrú (Santiago de Chile) MSC: 58C40 58J50 35P05 53C21 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nakkajima, Yukiyoshi; Yobuko, Fuetaro Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic \(p>0\) and log weak Lefschetz conjecture for log crystalline cohomologies. (English) Zbl 1498.14046 Eur. J. Math. 7, No. 4, 1537-1615 (2021). Reviewer: Dingxin Zhang (Beijing) MSC: 14F30 14F40 14J32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Halpern-Leistner, Daniel; Pomerleano, Daniel Equivariant Hodge theory and noncommutative geometry. (English) Zbl 1460.14005 Geom. Topol. 24, No. 5, 2361-2433 (2020). Reviewer: Jonas McCandless (Münster) MSC: 14A22 14C30 19D55 19L47 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sheng, Mao; Shentu, Junchao On \(E_1\)-degeneration for the special fiber of a semistable family. (English) Zbl 1462.14025 Commun. Number Theory Phys. 14, No. 3, 555-584 (2020). Reviewer: Alexander Petrov (Cambridge) MSC: 14F40 14C30 14D06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mondal, Chandan Kumar; Shaikh, Absos Ali Some results in \(\eta \)-Ricci soliton and gradient \(\rho \)-Einstein soliton in a complete Riemannian manifold. (English) Zbl 1429.53043 Commun. Korean Math. Soc. 34, No. 4, 1279-1287 (2019). MSC: 53C15 53C21 53E20 58E20 58J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hintz, Peter; Vasy, András Asymptotics for the wave equation on differential forms on Kerr-de Sitter space. (English) Zbl 1401.53057 J. Differ. Geom. 110, No. 2, 221-279 (2018). Reviewer: Anthony D. Osborne (Keele) MSC: 53C50 35Q61 83C22 58A14 × Cite Format Result Cite Review PDF Full Text: arXiv Euclid
Rahimizadeh, Hooman; Sholar, Stan; Berg, Michael Toward quantizing quantum mechanical systems using Hodge-de Rham theory. (English) Zbl 1357.81169 JP J. Geom. Topol. 19, No. 3, 249-266 (2016). MSC: 81V70 81S10 14F40 33E12 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Tai-Wei; Ho, Chung-I; Teh, Jyh-Haur \(E_1\)-degeneration and \(d'd''\)-lemma. (English) Zbl 1389.55004 Commentat. Math. Univ. Carol. 57, No. 2, 155-162 (2016). MSC: 55T05 53C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fathizadeh, Farzad; Gabriel, Olivier On the Chern-Gauss-Bonnet theorem and conformally twisted spectral triples for \(C^*\)-dynamical systems. (English) Zbl 1335.58005 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 016, 21 p. (2016). MSC: 58B34 47B25 46L05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bello, Jason; Li, Yiran; Strichartz, Robert S. Hodge-de Rham theory of \(k\)-forms on carpet type fractals. (English) Zbl 1323.28008 Balan, Radu (ed.) et al., Excursions in harmonic analysis, Volume 3. The February Fourier talks at the Norbert Wiener Center, College Park, MD, USA, 2002–2013. Cham: Birkhäuser/Springer (ISBN 978-3-319-13229-7/hbk; 978-3-319-13230-3/ebook). Applied and Numerical Harmonic Analysis, 23-62 (2015). MSC: 28A80 × Cite Format Result Cite Review PDF Full Text: DOI
Anné, Colette; Takahashi, Junya Partial collapsing and the spectrum of the Hodge-de Rham operator. (English) Zbl 1329.58024 Anal. PDE 8, No. 5, 1025-1050 (2015). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 35P15 53C23 58J32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kirschner, Tim Period mappings with applications to symplectic complex spaces. (English) Zbl 1346.14042 Lecture Notes in Mathematics 2140. Cham: Springer (ISBN 978-3-319-17520-1/pbk; 978-3-319-17521-8/ebook). xviii, 275 p. (2015). Reviewer: Ruifang Song (Mountain View) MSC: 14F05 32C20 32S35 14C34 14-02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Demlow, Alan; Hirani, Anil N. A posteriori error estimates for finite element exterior calculus: the de Rham complex. (English) Zbl 1308.65187 Found. Comput. Math. 14, No. 6, 1337-1371 (2014). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N15 65N30 58A12 58A14 58A15 58J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Aaron, Skye; Conn, Zach; Strichartz, Robert S.; Yu, Hui Hodge-de Rham theory on fractal graphs and fractals. (English) Zbl 1279.28011 Commun. Pure Appl. Anal. 13, No. 2, 903-928 (2014). MSC: 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ilias, Saïd; Makhoul, Ola A generalization of a Levitin and Parnovski universal inequality for eigenvalues. (English) Zbl 1252.35212 J. Geom. Anal. 22, No. 1, 206-222 (2012). MSC: 35P15 58J50 58C40 58A10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anné, Colette; Takahashi, Junya \(p\)-spectrum and collapsing of connected sums. (English) Zbl 1254.58012 Trans. Am. Math. Soc. 364, No. 4, 1711-1735 (2012). Reviewer: Wolfram Bauer (Göttingen) MSC: 58J50 35P15 53C23 58J32 × Cite Format Result Cite Review PDF Full Text: DOI
Bracken, Paul The Hodge-de Rham decomposition theorem and an application to a partial differential equation. (English) Zbl 1299.58004 Acta Math. Hung. 133, No. 4, 332-341 (2011). Reviewer: Andrew Bucki (Edmond) MSC: 58A14 58A10 47J05 35R01 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Delanghe, Richard; Lávička, Roman; Souček, Vladimír On polynomial solutions of generalized Moisil-Théodoresco systems and Hodge-de Rham systems. (English) Zbl 1254.30083 Adv. Appl. Clifford Algebr. 21, No. 3, 521-530 (2011). MSC: 30G35 31C99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Lalescu, Virgil-Dacian; Stretcu, Daniel Spectral properties of Hodge-de Rham like operators associated to a smooth \((1;1)\)-tensor field and harmonic theory. (English) Zbl 1224.58020 An. Univ. Vest Timiș., Ser. Mat.-Inform. 48, No. 1-2, 189-204 (2010). MSC: 58J10 58J50 58J35 × Cite Format Result Cite Review PDF
Albici, Mihaela Smooth dependence on Riemannian metric of eigenvalues of Hodge-de Rham operators. (English) Zbl 1240.58015 Sci. Stud. Res., Ser. Math. Inform. 19, No. 2, 7-20 (2009). MSC: 58J10 58J50 58A14 × Cite Format Result Cite Review PDF
Petrişor, Camelia-Ionela A commuting property for generalized Hodge-de Rham operators. (English) Zbl 1221.58002 Tensor, New Ser. 71, No. 2, 143-150 (2009). MSC: 58A14 53C21 58A10 × Cite Format Result Cite Review PDF
Ilias, Said; Makhoul, Ola ‘Universal’ inequalities for the eigenvalues of the Hodge de Rham Laplacian. (English) Zbl 1178.35277 Ann. Global Anal. Geom. 36, No. 2, 191-204 (2009). MSC: 35P15 58J50 58A10 × Cite Format Result Cite Review PDF Full Text: DOI
Jammes, Pierre On the multiplicity of eigenvalues of a compact manifold. (Sur la multiplicité des valeurs propres d’une variété compacte.) (French) Zbl 1235.58022 Actes de Séminaire de Théorie Spectrale et Géométrie. Année 2007–2008. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Séminaire de Théorie Spectrale et Géométrie 26, 1-11 (2008). MSC: 58J50 × Cite Format Result Cite Review PDF Full Text: EuDML
Turmacu, Mihaela Remarks concerning continuity and smoothness properties of the eigenvalues of Hodge-de Rham operators with respect to the Riemannian metric. (English) Zbl 1174.58007 Andrica, Dorin (ed.) et al., Contemporary geometry and topology and related topics. Proceedings of the 8th international workshop on differential geometry and its applications, Cluj-Napoca, Romania, August 19–25, 2005. Cluj-Napoca: Cluj University Press. 283-287 (2008). Reviewer: Jesus Alvarez Lopez (Santiago de Compostela) MSC: 58J10 58J50 58A14 × Cite Format Result Cite Review PDF
Jammes, Pierre Prescribing the spectrum of a Hodge-de Rham Laplacian within a conformal class. (Prescription du spectre du laplacien de Hodge-de Rham dans une classe conforme.) (French) Zbl 1155.58305 Comment. Math. Helv. 83, No. 3, 521-537 (2008). Reviewer: Witold Mozgawa (Lublin) MSC: 58J50 58C40 53A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Craioveanu, Mircea; Lalescu, Virgil-Dacian; Petrişor, Camelia-Ionela Spectral properties of a class of Hodge-De Rham like operators. (English) Zbl 1199.58013 An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 53, Suppl., 107-122 (2007). MSC: 58J10 58J50 58J35 × Cite Format Result Cite Review PDF
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Shapiro, Michael The Cauchy transform for the Hodge/de Rham system and some of its properties. (English) Zbl 1219.30018 Georgian Math. J. 14, No. 1, 1-20 (2007). Reviewer: Messoud A. Efendiev (Berlin) MSC: 30E20 30E25 30G35 58A14 × Cite Format Result Cite Review PDF
Prykarpatsky, Yarema A.; Samoilenko, Anatoliy M.; Prykarpatsky, Anatoliy K. A survey of the spectral and differential geometric aspects of the generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems. I. (English) Zbl 1105.58009 Appl. Math. E-Notes 5, 210-246 (2005). Reviewer: Mircea Puta (Timişoara) MSC: 58J10 58A12 47B40 34A26 34A30 34B15 × Cite Format Result Cite Review PDF Full Text: EuDML
Bruna, Joaquim; Girbau, Joan Mapping properties of the Laplacian in Sobolev spaces of forms on complete hyperbolic manifolds. (English) Zbl 1059.58016 Ann. Global Anal. Geom. 25, No. 2, 151-176 (2004). Reviewer: J. Eichhorn (Greifswald) MSC: 58J05 53C21 58J50 58J70 × Cite Format Result Cite Review PDF Full Text: DOI
Caspar, Alexander Kummer-Chern-Eisenstein motives via Hilbert modular surfaces. (English) Zbl 1026.11049 Bonner Mathematische Schriften. 358. Bonn: Univ. Bonn, Mathematisches Institut (Diss.), 100 p. (2003). Reviewer: Werner Kleinert (Berlin) MSC: 11F41 11G18 14G35 14F42 19E15 × Cite Format Result Cite Review PDF
Carron, Gilles A topological criterion for the existence of half-bound states. (English) Zbl 1027.58023 J. Lond. Math. Soc., II. Ser. 65, No. 3, 757-768 (2002). Reviewer: Ricardo Sa Earp (Rio de Janeiro) MSC: 58J50 × Cite Format Result Cite Review PDF Full Text: DOI
Zavada, K. G.; Shamarov, N. N. De Rham-Hodge-Kodaira decomposition on an infinite-dimensional space with a smooth product-measure. (English. Russian original) Zbl 0990.58003 Mosc. Univ. Math. Bull. 55, No. 4, 14-18 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 4, 14-18 (2000). Reviewer: V.V.Vlasov (Moskva) MSC: 58A12 58A14 58A10 × Cite Format Result Cite Review PDF
Boucetta, Mohamed Spectrum of the Lichnerowicz Laplacians on the spheres and the real projective spaces. (Spectre des Laplacien de Lichnerowicz sur les sphères et les projectifs réels.) (French) Zbl 0964.58024 Publ. Mat., Barc. 43, No. 2, 451-483 (1999). Reviewer: Mircea Craioveanu (Timişoara) MSC: 58J50 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Pedon, Emmanuel Harmonic analysis for differential forms on complex hyperbolic spaces. (English) Zbl 0935.22010 J. Geom. Phys. 32, No. 2, 102-130 (1999). Reviewer: Adela-Gabriela Oiaga (Bucureşti) MSC: 22E30 43A85 58A10 58C40 22E46 43A90 32M15 × Cite Format Result Cite Review PDF Full Text: DOI
Wünsch, V. On Huygens’ principle for the Hodge-de Rham equations with Lorentzian gauge. (English) Zbl 0876.58049 Z. Anal. Anwend. 16, No. 1, 59-72 (1997). Reviewer: V.Perlick (Berlin) MSC: 58J45 83C50 35B30 53B30 × Cite Format Result Cite Review PDF Full Text: DOI
Elizalde, E.; Lygren, M.; Vassilevich, D. V. Antisymmetric tensor fields on spheres: Functional determinants and nonlocal counterterms. (English) Zbl 0863.58071 J. Math. Phys. 37, No. 7, 3105-3117 (1996). MSC: 58J50 58J52 83E50 81Q10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alexandrov, Sergei; Vassilevich, Dmitri Heat kernel for nonminimal operators on a Kähler manifold. (English) Zbl 0859.58027 J. Math. Phys. 37, No. 11, 5715-5718 (1996). MSC: 58J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Schick, Thomas Analysis on \(\delta\)-manifolds of bounded geometry, Hodge-de Rham isomorphism and \(L^2\)-index theorem. (English) Zbl 0910.58003 Berichte aus der Mathematik. Aachen: Shaker Verlag. ii, 111 p. (1996). Reviewer: E.Outerelo (Madrid) MSC: 58A12 58A14 58-02 × Cite Format Result Cite Review PDF
de Azcárraga, José A.; Izquierdo, José M. Lie groups, Lie algebras, cohomology and some applications in physics. (English) Zbl 0836.22027 Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge Univ. Press. xvii, 455 p. (1995). Reviewer: A.A.Bogush (Minsk) MSC: 22E60 17B56 17B65 17B67 57T10 81R10 17B68 81T13 17-02 22-02 20J06 20J05 × Cite Format Result Cite Review PDF
Bordoni, Manlio Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds. (English) Zbl 0791.58094 Math. Ann. 298, No. 4, 693-718 (1994). Reviewer: M.Bordoni (Roma) MSC: 58J50 35P15 53C20 53C27 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Craioveanu, M.; Puta, M.; Rassias, Themistocles M. On the geometry of the Hodge-De Rham Laplace operators. (English) Zbl 0879.58075 Pràstaro, A. (ed.) et al., Geometry in partial differential equations. Singapore: World Scientific. 51-67 (1994). MSC: 58J50 58J05 × Cite Format Result Cite Review PDF
Harder, Günter Eisenstein cohomology and the construction of mixed motives. (Eisensteinkohomologie und die Konstruktion gemischter Motive.) (English) Zbl 0795.11024 Lecture Notes in Mathematics. 1562. Berlin: Springer-Verlag. xx, 184 p. DM 52.00; öS 405.60; sFr. 57.50 /sc (1993). Reviewer: J.Schwermer (Eichstätt) MSC: 11F67 11F75 11F80 11-02 14G35 14F99 11G18 11G40 × Cite Format Result Cite Review PDF
Atiyah, Michael On the work of Edward Witten. (English) Zbl 0742.01013 Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 31-35 (1991). Reviewer: Ü.Lumiste (Tartu) MSC: 01A60 01A70 × Cite Format Result Cite Review PDF
Cordero, Luis A.; Fernández, Marisa; Gray, Alfred The Frölicher spectral sequence for compact nilmanifolds. (English) Zbl 0721.58003 Ill. J. Math. 35, No. 1, 56-67 (1991). Reviewer: G.Arca (Cagliari) MSC: 58A14 58C40 32M10 53C15 58A12 × Cite Format Result Cite Review PDF
Nishikawa, Seiki; Ramachandran, Mohan; Tondeur, Philippe The heat equation for Riemannian foliations. (English) Zbl 0702.58074 Trans. Am. Math. Soc. 319, No. 2, 619-630 (1990). Reviewer: L.Nicolaescu MSC: 58J35 35K05 58A14 × Cite Format Result Cite Review PDF Full Text: DOI
Pittie, Harsh V. The nondegeneration of the Hodge-de Rham spectral sequence. (English) Zbl 0671.32024 Bull. Am. Math. Soc., New Ser. 20, No. 1, 19-22 (1989). Reviewer: F.Campana MSC: 32M10 32Q99 58A14 × Cite Format Result Cite Review PDF Full Text: DOI
Gallot, S.; Meyer, D. D’un résultat Hilbertien à un principe de comparaison entre spectres. Applications. (On a result of Hilbert concerning a comparison principle between spectra. Applications). (French) Zbl 0673.58045 Ann. Sci. Éc. Norm. Supér. (4) 21, No. 4, 561-591 (1988). Reviewer: M.Craioveanu MSC: 58J50 53C20 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Helffer, B.; Sjöstrand, J. Puits multiples en mécanique semi-classique. IV: Étude du complexe de Witten. (Multiple wells in semi-classical limit. IV: Investigation of the Witten complex). (French) Zbl 0597.35024 Commun. Partial Differ. Equations 10, 245-340 (1985). Reviewer: J.Chrastina MSC: 35J10 58J50 58E05 × Cite Format Result Cite Review PDF Full Text: DOI
Warner, N. P. The application of Regge calculus to quantum gravity and quantum field theory in a curved background. (English) Zbl 0494.53054 Proc. R. Soc. Lond., Ser. A 383, 359-377 (1982). MSC: 53C80 06B30 81T08 × Cite Format Result Cite Review PDF Full Text: DOI
Obădeanu, Virgil Applications of exterior differential forms in mechanics and electrodynamics. (Aplicaţii ale formelor diferenţiale exterioare în mecanică şi electrodinamică). (Romanian. French summary) Zbl 0569.70001 Monografii Matematice, 15. Timișoara: Universitatea din Timișoara, Facultatea de Științe ale Naturii, Secția Matematică. V, 143 p. (1981). MSC: 70-02 78-02 53B50 83A05 × Cite Format Result Cite Review PDF