Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds

Yasuaki Fujitani; Yohei Sakurai

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arXiv · 2408.15744

Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds

Yasuaki Fujitani·Yohei Sakurai

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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.

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Yasuaki Fujitani, Yohei Sakurai. 2024-08-28. Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds. https://arxiv.org/abs/2408.15744

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