Gradient estimates and the first Neumann eigenvalue on manifolds with boundary

DOI10.1016/j.spa.2005.04.004zbMath1088.58015OpenAlexW2061268440MaRDI QIDQ2567227

Feng-Yu Wang

Publication date: 29 September 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2005.04.004

zbMATH Keywords

Neumann semigroup

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65)

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Cites Work

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• The radial part of Brownian motion on a manifold: A semimartingale property
• Application of coupling method to the first eigenvalue on manifold
• Application of coupling methods to the Neumann eigenvalue problem
• Multiplicative functional for the heat equation on manifolds with boundary.
• Probability distance inequalities on Riemannian manifolds and path spaces.
• Some new results on eigenvectors via dimension, diameter, and Ricci curvature
• Gradient estimates of Dirichlet heat semigroups and application to isoperimetric inequalities.
• Equivalence of dimension-free Harnack inequality and curvature condition
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• A gradient estimate on a manifold with convex boundary
• On Poincaré Type Inequalities
• Neumann Eigenvalue Estimate on a Compact Riemannian Manifold
• A Simple Analytic Proof of an Inequality by P. Buser
• The geometry of Markov diffusion generators