Manifolds close to the round sphere

Valery Marenich

doi:10.1215/ijm/1258138359

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Home > Journals > Illinois J. Math. > Volume 45 > Issue 2 > Article

Summer 2001 Manifolds close to the round sphere

Valery Marenich

Illinois J. Math. 45(2): 615-629 (Summer 2001). DOI: 10.1215/ijm/1258138359

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Abstract

We prove that the manifold of minimal radial curvature is homeomorphic to the sphere if its radius or volume is larger than half the radius or volume of the round sphere of constant curvature . These results are optimal and give a complete generalization of the corresponding results for manifolds of sectional curvature bounded from below.