Rigidity Phenomena in Manifolds with Boundary Under a Lower Weighted Ricci Curvature Bound

Yohei Sakurai

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1 Citation (Scopus)

Abstract

We study Riemannian manifolds with boundary under a lower N-weighted Ricci curvature bound for N at most 1, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and various splitting theorems. We also obtain rigidity theorems for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.

Original languageEnglish
JournalJournal of Geometric Analysis
Volume29
Issue number1
DOIs
Publication statusPublished - 2019 Jan 15

Keywords

  • Manifold with boundary
  • Weighted Ricci curvature
  • Weighted p-Laplacian

ASJC Scopus subject areas

  • Geometry and Topology

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