Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds
Differential Geometry
2023-08-01 v1
Abstract
In this article, we investigate the rate at which the first Dirichlet eigenvalue of geodesic balls decreases as the radius approaches infinity. We prove that if the conformal infinity of an asymptotically hyperbolic Einstein manifold is of nonnegative Yamabe type, then the two-term asymptotic of the eigenvalues is the same as that in hyperbolic space.
Keywords
Cite
@article{arxiv.2307.16439,
title = {Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds},
author = {Xiaoshang Jin},
journal= {arXiv preprint arXiv:2307.16439},
year = {2023}
}
Comments
12 pages