Rigidity of manifolds with boundary under a lower bakry-& mery ricci curvature bound

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2 Citations (Scopus)

Abstract

We study Riemannian manifolds with boundary under a lower Bakry- Emery 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 theorems for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.

Original languageEnglish
Pages (from-to)69-109
Number of pages41
JournalTohoku Mathematical Journal
Volume71
Issue number1
DOIs
Publication statusPublished - 2019 Mar

Keywords

  • Bakry-emery ricci curvature
  • Manifold with boundary

ASJC Scopus subject areas

  • Mathematics(all)

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