Lectures on Nonsmooth Differential Geometry 2020 Edition Contributor(s): Gigli, Nicola (Author), Pasqualetto, Enrico (Author) |
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ISBN: 3030386155 ISBN-13: 9783030386153 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback - Other Formats Published: February 2021 |
Additional Information |
BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Calculus - Mathematics | Mathematical Analysis |
Physical Information: 0.46" H x 6.14" W x 9.21" (0.69 lbs) 204 pages |
Descriptions, Reviews, Etc. |
Publisher 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. |