Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds
Yasuaki Fujitani, Yohei Sakurai
公開日: 2024/8/28
Abstract
We develop geometric analysis on weighted Riemannian manifolds under lower $0$-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang-Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi-Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type.