9783030386153-3030386155-Lectures on Nonsmooth Differential Geometry (SISSA Springer Series)

Lectures on Nonsmooth Differential Geometry (SISSA Springer Series)

ISBN-13: 9783030386153
ISBN-10: 3030386155
Edition: 1st ed. 2020
Author: Nicola Gigli
Publication date: 2021
Publisher: Springer
Format: Paperback 216 pages
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Book details

ISBN-13: 9783030386153
ISBN-10: 3030386155
Edition: 1st ed. 2020
Author: Nicola Gigli
Publication date: 2021
Publisher: Springer
Format: Paperback 216 pages

Summary

Lectures on Nonsmooth Differential Geometry (SISSA Springer Series) (ISBN-13: 9783030386153 and ISBN-10: 3030386155), written by authors Nicola Gigli, was published by Springer in 2021. With an overall rating of 4.1 stars, it's a notable title among other Geometry & Topology (Mathematics) books. You can easily purchase or rent Lectures on Nonsmooth Differential Geometry (SISSA Springer Series) (Paperback) from BooksRun, along with many other new and used Geometry & Topology books and textbooks. And, if you're looking to sell your copy, our current buyback offer is $0.3.

Description

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.

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