Lectures on nonsmooth differential geometry / Nicola Gigli, Enrico Pasqualetto.
2020
QA641
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Title
Lectures on nonsmooth differential geometry / Nicola Gigli, Enrico Pasqualetto.
Author
Gigli, Nicola.
ISBN
9783030386139
3030386139
9783030386122
3030386139
9783030386122
Publication Details
Cham : Springer, 2020.
Language
English
Description
1 online resource (212 pages).
Item Number
10.1007/978-3-030-38
Call Number
QA641
Dewey Decimal Classification
516.3/6
Summary
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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Source of Description
Description based on print version record.
Added Author
Pasqualetto, Enrico.
Series
SISSA Springer series ; v. 2.
Available in Other Form
Lectures on Nonsmooth Differential Geometry
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