Kokarev, G (2020) Conformal volume and eigenvalue problems. Indiana University Mathematics Journal, 69. pp. 1975-2003. ISSN 0022-2518
Abstract
We prove inequalities for Laplace eigenvalues on Riemannian manifolds generalising to higher eigenvalues two classical inequalities for the first Laplace eigenvalue - the inequality in terms of the L2-norm of mean curvature, due to Reilly in 1977, and the inequality in terms of conformal volume, due to Li and Yau in 1982, and El Soufi and Ilias in 1986. We also obtain bounds for the number of negative eigenvalues of Schrödinger operators, and in particular, index bounds for minimal hypersurfaces in spheres.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Laplace eigenvalues; conformal volume; eigenvalue inequalities; minimal hypersurface |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 May 2019 09:22 |
Last Modified: | 11 Nov 2020 16:46 |
Status: | Published |
Publisher: | Indiana University Press |
Identification Number: | 10.1512/iumj.2020.69.8021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:146223 |
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