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The C1,1 conclusions in Gromov's theory

Published online by Cambridge University Press:  19 September 2008

Charles C. Pugh
Charles C. Pugh
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, California 94720, USA
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Abstract

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According to M. Gromov, any sequence of Riemann manifolds with uniformly bounded geometry has a subsequence that converges to a limit. It is shown here that this limit Riemann structure is Lipschitz, generates a Lipschitz geodesic flow, and consequently, as Gromov asserted, the limit distance function is of class C1,1. Sharpness of the results is discussed. A simple, extrinsic proof of Gromov's Theorem is included.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 1 , March 1987 , pp. 133 - 147
Copyright
Copyright © Cambridge University Press 1987

References

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