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Title: Lectures on Nonsmooth Differential Geometry ([EBook]) / by Nicola Gigli, Enrico Pasqualetto. Dewey Class: 516.36 Author: Gigli, Nicola., 1979- author. Edition statement: 1st ed. 2020. Added Personal Name: Pasqualetto, Enrico. author. Publication: Cham : Springer International Publishing, 2020. Other name(s): SpringerLink (Online service) Physical Details: XI, 204 p. 8 illus. : online resource. Series: SISSA Springer Series,2524-857X ;; 2 ISBN: 9783030386139 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). 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. ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
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