Heat kernel bounds on manifolds with cusps
type: Item
instance of: scholarly article
title: Heat kernel bounds on manifolds with cusps
zbMATH Open document ID: 0629.53044
DOI: 10.1016/0022-1236(87)90098-X
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: The authors obtain pointwise upper bounds for the heat kernel of a Riemannian manifold with cusps. They discuss a class of manifolds which have bounded geometry with respect to a hyperbolic structure with cusps; these manifolds include asymptotically hyperbolic manifolds. They obtain upper bounds on the heat kernels which they believe to be nearly optimal. They use methods of Gross to derive the required bounds from suitable Sobolev inequalities and logarithmic Sobolev inequalities.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 4024228
zbMATH Keywords: heat kernel
zbMATH Keywords: Riemannian manifold with cusps
zbMATH Keywords: bounded geometry
zbMATH Keywords: hyperbolic structure
zbMATH Keywords: Sobolev inequalities
author: E. Brian Davies
author: Nikolaos Mandouvalos
reviewed by: Peter B. Gilkey
MaRDI profile type: Publication
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full work available at URL: 0022-1236(87)90098-x
OpenAlex ID: W2094914735
description: scientific article; zbMATH DE number 4024228