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Bibliographic Details
Main Authors:	Fujitani, Yasuaki, Sakurai, Yohei
Format:	Preprint
Published:	2024
Subjects:	Differential Geometry
Online Access:	https://arxiv.org/abs/2408.15744
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Table of Contents:

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.