A topological splitting theorem for weighted Alexandrov spaces

Kazuhiro Kuwae, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting theorem for Riemannian manifolds with singularities of nonnegative (Bakry-Emery) Ricci curvature.

Original languageEnglish
Pages (from-to)59-76
Number of pages18
JournalTohoku Mathematical Journal
Volume63
Issue number1
DOIs
Publication statusPublished - 2011 Mar

Keywords

  • Bishop-Gromov inequality
  • Ricci curvature
  • Splitting theorem

ASJC Scopus subject areas

  • Mathematics(all)

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