This is an announcement for the paper "Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property" by Jeff Cheeger and Bruce Kleiner.

Abstract: We prove the differentiability of Lipschitz maps X---->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar'e inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direction of tangent vectors to suitable rectifiable curves.

Archive classification: math.MG math.DG math.FA

Mathematics Subject Classification: 46B22 (primary), 46G05 (secondary)

The source file(s), pirnp.bbl: 3004 bytes

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0808.3249

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http://arXiv.org/abs/0808.3249

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