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 cur- vature bounded from below a second order calculus can be developed, permitting to define Hessian, covariant/exterior derivatives and Ricci curvature.
Nonsmooth differential geometry : an approach tailored for spaces with Ricci curvature bounded from below / Gigli, Nicola. - In: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0065-9266. - 251:1196(2018), pp. 1-174. [10.1090/memo/1196]
Nonsmooth differential geometry : an approach tailored for spaces with Ricci curvature bounded from below
Gigli, Nicola
2018-01-01
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 cur- vature bounded from below a second order calculus can be developed, permitting to define Hessian, covariant/exterior derivatives and Ricci curvature.File in questo prodotto:
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