Surgery of the Faber-Krahn inequality and applications to heat kernel bounds

DOI10.1016/j.na.2015.10.006zbMath1334.58019OpenAlexW2582031834MaRDI QIDQ897363

Alexander Grigor'yan, Laurent Saloff-Coste

Publication date: 17 December 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.10.006

zbMATH Keywords

Laplace-Beltrami operatorheat kernelFaber-Krahn inequalityfirst Dirichlet eigenvalue

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items

Sobolev-type inequalities on Cartan-Hadamard manifolds and applications to some nonlinear diffusion equations, Heat kernel estimates on spaces with varying dimension, Lower bound of Schrödinger operators on Riemannian manifolds, Poincaré constant on manifolds with ends, Heat kernel estimates on Harnack manifolds and beyond, Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end, Riesz transform via heat kernel and harmonic functions on non-compact manifolds, Nonexistence of Radial Optimal Functions for the Sobolev Inequality on Cartan-Hadamard Manifolds, Heat kernel estimates on connected sums of parabolic manifolds, Hardy's inequality and Green function on metric measure spaces, Asymptotic properties of solutions to the Cauchy problem for degenerate parabolic equations with inhomogeneous density on manifolds, Riesz transforms on a class of non-doubling manifolds, Analysis and stochastic processes on metric measure spaces, Heat kernel on manifolds with ends, On-diagonal lower estimate of heat kernels for locally finite graphs and its application to the semilinear heat equations

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