Lectures on Nonsmooth Differential Geometry (Hardcover, 1st ed. 2020)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	SISSA Springer Series, 2
Release date:	February 2020
First published:	2020
Authors:	Nicola Gigli • Enrico Pasqualetto
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	204
Edition:	1st ed. 2020
ISBN-13:	978-3-03-038612-2
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-03-038612-0
Barcode:	9783030386122

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