Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold M. In the first series [KT1], we showed that all Busemann functions on an M which is not less curved than a von Mangoldt surface of revolution M̃ are exhaustions, if the total curvature of M̃ is greater than π. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to R 2 whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [KT1] to an M which is not less curved than a more general surface of revolution.

Original languageEnglish
Pages (from-to)185-200
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number1
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Busemann function
  • Radial curvature
  • Total curvature

ASJC Scopus subject areas

  • Mathematics(all)

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