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The C1,1 conclusions in Gromov's theory
Published online by Cambridge University Press: 19 September 2008
Abstract
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.
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- Copyright © Cambridge University Press 1987
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