Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds
Differential Geometry
2025-10-06 v2
Abstract
We develop geometric analysis on weighted Riemannian manifolds under lower -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.
Keywords
Cite
@article{arxiv.2408.15744,
title = {Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds},
author = {Yasuaki Fujitani and Yohei Sakurai},
journal= {arXiv preprint arXiv:2408.15744},
year = {2025}
}
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19 pages