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memo_has_moved_text();Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below

Nicola Gigli

Publication: Memoirs of the American Mathematical Society
Publication Year: 2018; Volume 251, Number 1196
ISBNs: 978-1-4704-2765-8 (print); 978-1-4704-4266-8 (online)
DOI: https://doi.org/10.1090/memo/1196
Published electronically: November 6, 2017

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Chapters

• Introduction
• Chapter 1. The machinery of $L^p(\mm )$-normed modules
• Chapter 2. First order differential structure of general metric measure spaces
• Chapter 3. Second order differential structureof $\RCD (K,\infty )$ spaces

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.