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

About this Title

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)
Published electronically: November 6, 2017

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Table of Contents


  • 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


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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