Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds
type: Item
instance of: scholarly article
title: Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds
author: Xiaoshang Jin
published in: Bulletin of the London Mathematical Society
publication date: 2024-10-08T00:00:00Z
review text: The paper contains two main results on the rate at which the first Dirichlet eigenvalue of the Laplace-Beltrami operator on geodesic balls of certain manifolds with conformal infinity decreases as the radius goes to infinity. In particular, it is shown 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:\N\[\N\forall p \in (M^{n+1}g):\ \ \lambda_1(B(p,R))=\frac{n^2}{4} + \frac{\pi^2}{R^2} + O (R^{-3}),\ \ {\hbox{for}}\ \ R \ {\hbox{sufficiently large}}.\N\]
reviewed by: Alina Stancu
Mathematics Subject Classification ID: 53C18
Mathematics Subject Classification ID: 58C40
zbMATH DE Number: 7922702
zbMATH Keywords: asymptotically hyperbolic manifolds
zbMATH Keywords: Einstein manifolds
zbMATH Keywords: first Dirichlet eigenvalue
zbMATH Keywords: Yamabe type
MaRDI profile type: Publication
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DOI: 10.1112/BLMS.13041
description: scientific article; zbMATH DE number 7922702