Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below: I

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We investigate the finiteness structure of a complete non-compact n-dimensional Riemannian manifold M whose radial curvature at a base point of M is bounded from below by that of a non-compact von Mangoldt surface of revolution with its total curvature greater than π. We show, as our main theorem, that all Busemann functions on M are exhaustions, and that there exists a compact subset of M such that the compact set contains all critical points for any Busemann function on M. As corollaries by the main theorem, M has finite topological type, and the isometry group of M is compact.

Original languageEnglish
Pages (from-to)251-266
Number of pages16
JournalMathematische Annalen
Volume351
Issue number2
DOIs
Publication statusPublished - Oct 2011
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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