Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method
Abstract
In this paper, we employ the ABP method developed by Brendle to establish the optimal $L^p$ logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp $L^2$ logarithmic Sobolev inequality for submanifolds in manifolds with nonnegative sectional curvature. The sharp constants in both inequalities depend on the asymptotic volume ratio of the ambient manifold.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Mathematical Inequalities and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 January 2026
- Document type
- Preprint