English

The Boundary between Compact and Noncompact Complete Riemann Manifolds

Differential Geometry 2007-05-23 v1

Abstract

In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of the infimum. Subsequently the curvature hypothesis has been weakened, and in this paper we weaken it further in an attempt to find the ultimate, sharp result.

Keywords

Cite

@article{arxiv.math/0501414,
  title  = {The Boundary between Compact and Noncompact Complete Riemann Manifolds},
  author = {D. Holcman and C. Pugh},
  journal= {arXiv preprint arXiv:math/0501414},
  year   = {2007}
}

Comments

24 pages,3 figures, good stuff. submitted

R2 v1 2026-07-22T17:14:51.671Z