03324nam 22005295 450 991048310280332120200706002830.03-030-38613-910.1007/978-3-030-38613-9(CKB)4100000010348638(DE-He213)978-3-030-38613-9(MiAaPQ)EBC6109028(PPN)242981003(EXLCZ)99410000001034863820200210d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierLectures on Nonsmooth Differential Geometry /by Nicola Gigli, Enrico Pasqualetto1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (XI, 204 p. 8 illus.) SISSA Springer Series,2524-857X ;23-030-38612-0 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.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.SISSA Springer Series,2524-857X ;2Differential geometryCalculusDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Calculushttps://scigraph.springernature.com/ontologies/product-market-codes/M12220Differential geometry.Calculus.Differential Geometry.Calculus.516.36Gigli Nicolaauthttp://id.loc.gov/vocabulary/relators/aut227784Pasqualetto Enricoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910483102803321Lectures on Nonsmooth Differential Geometry2311004UNINA