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arXiv · 1407.0809

Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below

Nicola Gigli
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Abstract

We discuss in which sense general metric measure spaces possess a first order differential structure. Building on this, we then see that on spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting to define Hessian, covariant/exterior derivatives and Ricci curvature.

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Nicola Gigli. 2014-07-03. Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below. https://arxiv.org/abs/1407.0809

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