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MARC 21

Lectures on Nonsmooth Differential Geometry
Tag	Description
020	$a9783030386139
082	$a516.36
099	$aOnline resource: Springer
100	$aGigli, Nicola.$d1979-$eauthor.
245	$aLectures on Nonsmooth Differential Geometry$h[EBook]$cby Nicola Gigli, Enrico Pasqualetto.
250	$a1st ed. 2020.
260	$aCham$bSpringer International Publishing$c2020.
300	$aXI, 204 p. 8 illus.$bonline resource.
336	$atext
338	$aonline resource
440	$aSISSA Springer Series,$x2524-857X ;$v2
505	$a1. 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.
520	$aThis 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.
533	$aDigital 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
538	$a- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aPasqualetto, Enrico.$eauthor.
710	$aSpringerLink (Online service)
856	$uhttps://doi.org/10.1007/978-3-030-38613-9