Nicola Gigli

(Author)

Lectures on Nonsmooth Differential Geometry (2020)Paperback - 2020, 11 February 2021

Lectures on Nonsmooth Differential Geometry (2020)
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Part of Series
Sissa Springer
Print Length
204 pages
Language
English
Publisher
Springer
Date Published
11 Feb 2021
ISBN-10
3030386155
ISBN-13
9783030386153

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.

Product Details

Authors:
Nicola GigliEnrico Pasqualetto
Book Edition:
2020
Book Format:
Paperback
Country of Origin:
NL
Date Published:
11 February 2021
Dimensions:
23.39 x 15.6 x 1.17 cm
ISBN-10:
3030386155
ISBN-13:
9783030386153
Language:
English
Location:
Cham
Pages:
204
Publisher:
Weight:
312.98 gm

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