JournalscmhVol. 74, No. 3pp. 456–466

Open manifolds with nonnegative Ricci curvature and large volume growth

  • Changyu Xia

    Universidade de Brasília, Brasília, Brazil
Open manifolds with nonnegative Ricci curvature and large volume growth cover
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Abstract

In this paper, we study complete open n-dimensional Riemannian manifolds with nonnegative Ricci curvature and large volume growth. We prove among other things that such a manifold is diffeomorphic to a Euclidean n-space RnR^n if its sectional curvature is bounded from below and the volume growth of geodesic balls around some point is not too far from that of the balls in RnR^n .

Cite this article

Changyu Xia, Open manifolds with nonnegative Ricci curvature and large volume growth. Comment. Math. Helv. 74 (1999), no. 3, pp. 456–466

DOI 10.1007/S000140050099