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[null,"1.","Record Nr.",null,"UNISA996418260603316"]
[null,null,"Autore",null,"Gigli Nicola"]
[null,null,"Titolo",null,"Lectures on Nonsmooth Differential Geometry [[electronic resource] /] / by Nicola Gigli, Enrico Pasqualetto"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020"]
[null,null,"ISBN",null,"3-030-38613-9"]
[null,null,"Edizione",null,"[1st ed. 2020.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XI, 204 p. 8 illus.)"]
[null,null,"Collana",null,"SISSA Springer Series, , 2524-857X ; ; 2"]
[null,null,"Disciplina",null,"516.36"]
[null,null,"Soggetti",null,"Differential geometry"]
[{"$nulls":4},"Calculus"]
[{"$nulls":4},"Differential Geometry"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","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."]