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COMPLETE MANIFOLDS WITH SECTIONAL CURVATURE BOUNDED BELOW AND LARGE VOLUME GROWTH

Published online by Cambridge University Press:  15 March 2002

CHANGYU XIA
CHANGYU XIA
Affiliation:
Departamento de Matemática-IE, Fundação Universidade de Brasília, Campus Universitário, 70910-900-Brasília-DF, [email protected]
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Abstract

This paper provides a proof that an n-dimensional complete open Riemannian manifold M with sectional curvature KM [ges ] −1 is diffeomorphic to a Euclidean n-space Rn if the volume growth of geodesic balls in M is close to that of the balls in an n-dimensional hyperbolic space Hn(−1) of sectional curvature −1.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 2 , March 2002 , pp. 229 - 235
Copyright
© 2002 The London Mathematical Society

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