Lieb-Thirring inequalities on manifolds with constant negative curvature
File(s)LTh_negative_curvature10.pdf (280.05 KB)
Accepted version
Author(s)
Ilyin, Alexei
Laptev, Ari
Weinmann, Timon
Type
Journal Article
Abstract
In this short note we prove Lieb–Thirring inequalities on manifolds with negative constant curvature. The discrete spectrum appears below the continuous spectrum
[(d − 1)2/4, ∞), where d is the dimension of the hyperbolic space. As an application we
obtain a Polya type inequality with not a sharp constant. An example of a 2D domain is ´
given for which numerical calculations suggest that the Polya inequality holds for it.
[(d − 1)2/4, ∞), where d is the dimension of the hyperbolic space. As an application we
obtain a Polya type inequality with not a sharp constant. An example of a 2D domain is ´
given for which numerical calculations suggest that the Polya inequality holds for it.
Date Issued
2024-02
Date Acceptance
2023-11-27
Citation
Journal of Geometric Analysis, 2024, 34 (2)
ISSN
1050-6926
Publisher
Springer
Journal / Book Title
Journal of Geometric Analysis
Volume
34
Issue
2
Copyright Statement
Copyright © 2024 Springer-Verlag. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s12220-023-01506-4
Identifier
https://link.springer.com/article/10.1007/s12220-023-01506-4
Subjects
BOUNDS
Dirichlet Laplacian
EIGENVALUES
Hyperbolic space
LAPLACE
Lieb-Thirring inequalities
Mathematics
Physical Sciences
Polya inequality
Science & Technology
SPECTRUM
Publication Status
Published
Article Number
62
Date Publish Online
2024-01-05