Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property

Details Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property

2008-08-24

arxiv.org/abs/0808.3249v1

Mathematics

Metric Geometry

Scientific paper

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.

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