Lectures on Nonsmooth Differential Geometry Hardback
by Nicola Gigli, Enrico Pasqualetto
Part of the SISSA Springer Series series
Hardback
- Information
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 acomprehensive 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.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:204 pages, 8 Illustrations, black and white; XI, 204 p. 8 illus.
- Publisher:Springer Nature Switzerland AG
- Publication Date:11/02/2020
- Category:
- ISBN:9783030386122
Other Formats
- EPUB from £19.54
- Paperback / softback from £23.29
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:204 pages, 8 Illustrations, black and white; XI, 204 p. 8 illus.
- Publisher:Springer Nature Switzerland AG
- Publication Date:11/02/2020
- Category:
- ISBN:9783030386122