Noncompact manifolds with nonnegative Ricci curvature

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let (M, d) be a metric space. For 0 < r < R, let G(p, r, R) be the group obtained by considering all loops based at a point p M whose image is contained in the closed ball of radius r and identifying two loops if there is a homotopy between them that is contained in the open ball of radius R. In this article we study the asymptotic behavior of the G(p, r, R) groups of complete open manifolds of nonnegative Ricci curvature. We also find relationships between the G(p, r, R) groups and tangent cones at infinity of a metric space and show that any tangent cone at infinity of a complete open manifold of nonnegative Ricci curvature and small linear diameter growth is its own universal cover.

Original languageEnglish (US)
Pages (from-to)535-550
Number of pages16
JournalJournal of Geometric Analysis
Volume16
Issue number3
DOIs
StatePublished - 2006

Keywords

  • Ricci curvature
  • asymptotically polar
  • fundamental group
  • noncompact manifold
  • ray density

ASJC Scopus subject areas

  • Geometry and Topology

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