The boundary between compact and noncompact complete Riemann manifolds
D. HolcmanCharles Pugh
53C1553C20Riemannian geometryasymptotic manifoldspositive Ricci curvatureextension of Myer's theorem
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.
Indiana University Mathematics Journal
2007
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10.1512/iumj.2007.56.2860
10.1512/iumj.2007.56.2860
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Indiana Univ. Math. J. 56 (2007) 437 - 458
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