Rigidity of manifolds with boundary under a lower Ricci curvature bound

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6 Citations (Scopus)

Abstract

We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and a lower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop-Gromov type concerning the volumes of the metric neighborhoods of the boundaries. We conclude several rigidity theorems. As one of them, we obtain a volume growth rigidity theorem. We also show a splitting theorem of Cheeger-Gromoll type under the assumption of the existence of a single ray.

Original languageEnglish
Pages (from-to)85-119
Number of pages35
JournalOsaka Journal of Mathematics
Volume54
Issue number1
Publication statusPublished - 2017 Jan
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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