Isoperimetry, decrease of the heat kernel and Riesz transformations: A counterexample

DOI10.1007/BF02559523zbMath0826.53035MaRDI QIDQ1329658

Thierry Coulhon, Michel Ledoux

Publication date: 8 September 1994

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

isoperimetric inequalityinjectivity radiusheat kernelSobolev inequalityRiesz transformationbounded sectional curvature

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (13)

Dimensions at infinity for Riemannian manifolds ⋮ On-diagonal lower bounds for heat kernels and Markov chains ⋮ The Riesz transformation on conical varieties ⋮ Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds ⋮ Smoothing effects for the porous medium equation on Cartan-Hadamard manifolds ⋮ Riesz transformations on a class of manifolds with conical singularities ⋮ Riesz transforms on compact Lie groups, spheres and Gauss space ⋮ Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs ⋮ Riesz transform and \(L^p\)-cohomology for manifolds with Euclidean ends ⋮ On the weak \(L ^{p }\)-Hodge decomposition and Beurling--Ahlfors transforms on complete Riemannian manifolds ⋮ Large scale Sobolev inequalities on metric measure spaces and applications ⋮ L p -Green potential estimates on noncompact Riemannian manifolds ⋮ Riesz transforms for $1\le p\le 2$

Cites Work

• Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
• Analysis on nilpotent groups
• Comparaison des champs de vecteurs et des puissances du Laplacien sur une variété Riemannienne à courbure non positive
• Hardy-Littlewood theory for semigroups
• On the parabolic kernel of the Schrödinger operator
• Modified isoperimetric constants, and large time heat diffusion in Riemannian manifolds
• Isoperimetricity for groups and manifolds
• Noyau de la chaleur et discrétisation d'une variété riemannienne. (Heat kernel and discretization of a Riemannian manifold)
• Isoperimetric Constants, the Geometry of Ends, and Large Time Heat Diffusion in Riemannian Manifolds
• A Simple Analytic Proof of an Inequality by P. Buser
• Manifolds of Negative Curvature
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Isoperimetry, decrease of the heat kernel and Riesz transformations: A counterexample