The Boundary between Compact and Noncompact Complete Riemann Manifolds

Details The Boundary between Compact and Noncompact Complete Riemann Manifolds The Boundary between Compact and Noncompact Complete Riemann Manifolds

2005-01-24

arxiv.org/abs/math/0501414v1

Mathematics

Differential Geometry

24 pages,3 figures, good stuff. submitted

Scientific paper

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.

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