Gradient estimates of Dirichlet heat semigroups and application to isoperimetric inequalities.

DOI10.1214/aop/1078415841zbMath1087.58017OpenAlexW2105125369MaRDI QIDQ1879859

Feng-Yu Wang

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1078415841

zbMATH Keywords

gradient estimateheat semigroupcouplingisoperimetric

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (11)

Lipschitz Regularity of Graph Laplacians on Random Data Clouds ⋮ Trends to equilibrium in total variation distance ⋮ HJB equations and stochastic control on half-spaces of Hilbert spaces ⋮ Estimates of the Kantorovich norm on manifolds ⋮ The stochastic Schwarz lemma on Kähler manifolds by couplings and its applications ⋮ Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions ⋮ Gradient estimates for the fundamental solution of Lévy type operator ⋮ Uniform gradient estimates on manifolds with a boundary and applications ⋮ Gradient estimates for Dirichlet parabolic problems in unbounded domains ⋮ Gradient estimates for diffusion semigroups with singular coefficients ⋮ Gradient estimates and the first Neumann eigenvalue on manifolds with boundary

Cites Work

• The radial part of Brownian motion on a manifold: A semimartingale property
• Lower bounds for the eigenvalues of Riemannian manifolds
• Gradient estimates on manifolds using coupling
• Gradient estimates for harmonic functions on regular domains in Riemannian manifolds
• Application of coupling method to the first eigenvalue on manifold
• Application of coupling methods to the Neumann eigenvalue problem
• On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups
• Estimates of Dirichlet heat kernels
• Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
• Functional inequalities for empty essential spectrum
• A gradient estimate on a manifold with convex boundary
• Nonnegative ricci curvature and the brownian coupling property
• A note on the isoperimetric constant
• A Simple Analytic Proof of an Inequality by P. Buser
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