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

Abstract

We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincaré 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.

Cited by in corpus (2)

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• Compression bounds for Lipschitz maps from the Heisenberg group to $L_1$