Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below
Differential Geometry
2014-07-04 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1407.0809,
title = {Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below},
author = {Nicola Gigli},
journal= {arXiv preprint arXiv:1407.0809},
year = {2014}
}