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Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Lectures on Nonsmooth Differential Geometry ([EBook]) / by Nicola Gigli, Enrico Pasqualetto.
Author	Gigli, Nicola. , 1979-
Added Personal Name	Pasqualetto, Enrico
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Cham : Springer International Publishing , 2020.
Physical Details	XI, 204 p. 8 illus. : online resource.
Series	SISSA Springer Series 2524-857X ; ; 2
ISBN	9783030386139
Summary Note	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.:
Contents note	1. Preliminaries -- 2. Sobolev calculus on metric measure spaces -- 3. The theory of normed modules -- 4. First-order calculus on metric measure spaces -- 5. Heat ﬂow on metric measure spaces -- 6. Second-order calculus on RCD spaces -- 7. Appendix A: Functional analytic tools -- 8. Appendix B: Solutions to the exercises.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-38613-9
Links to Related Works	Subject References: Calculus . Differential Geometry . Authors: author . Gigli, Nicola. 1979- . Pasqualetto, Enrico . Corporate Authors: SpringerLink (Online service) . Series: SISSA Springer Series . Classification: 516.36 . 516.36 (DDC 23) .

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Lectures on Nonsmooth Differential Geometry

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