Modified Curvatures on Manifolds with Boundary and Applications

2011/02/17 by Feng‐Yu Wang, Wang, Feng-Yu
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1102.3552

openalex publication_date 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To study the reflecting diffusion processes on manifolds with boundary, some new curvature operators are introduced by using the Bakry-Emery curvature and the second fundamental form. As applications, the gradient estimates, log-Harnack inequality and Poincaré/log-Sobolev inequalities are investigated for the Neumann semigroup on manifolds with boundary.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• Semigroup Properties for the Second Fundamental Form

Related

• Pointwise Characterizations of Curvature and Second Fundamental Form on Riemannian Manifolds
• Reflecting Diffusion Process on Time-Inhomogeneous Manifolds with Boundary
• Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound
• Uniform gradient estimates on manifolds with a boundary and applications
• Gradient Estimate and Harnack Inequality on Non-Compact Riemannian Manifolds