Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound

2015/06/10 by Yohei Sakurai, Sakurai, Yohei
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1506.03223

openalex publication_date 2015/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study Riemannian manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and various splitting theorems. We also obtain rigidity results for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• A Picone's identity for the p-Laplacian and applications
• Normal and Integral Currents
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• The splitting theorem in non-smooth context

Related

• Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound
• Rigidity of manifolds with boundary under a lower Ricci curvature bound
• Boundary Effect of Ricci Curvature
• On Riemannian manifolds with positive weighted Ricci curvature of negative effective dimension
• On a conjecture of Schroeder and Strake