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arXiv · 1807.10063

Differential of metric valued Sobolev maps

Nicola Gigli·Enrico Pasqualetto·Elefterios Soultanis
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Abstract

We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.

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Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis. 2018-07-26. Differential of metric valued Sobolev maps. https://arxiv.org/abs/1807.10063

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