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

2024/08/28 by Yasuaki Fujitani, Fujitani, Yasuaki, Yohei Sakurai +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2408.15744

openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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.

Cited by

• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound
• Choi-Wang inequality for affine connections
• Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature

Related

• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound
• Eigenvalue estimates and applications on weighted manifolds
• A Steklov eigenvalue estimate for affine connections and its application to substatic triples
• Weighted Sobolev inequalities and Ricci flat manifolds
• Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound