LEADER 03349nam 22005295 450 001 996418260603316 005 20200706002830.0 010 $a3-030-38613-9 024 7 $a10.1007/978-3-030-38613-9 035 $a(CKB)4100000010348638 035 $a(DE-He213)978-3-030-38613-9 035 $a(MiAaPQ)EBC6109028 035 $a(PPN)242981003 035 $a(EXLCZ)994100000010348638 100 $a20200210d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Nonsmooth Differential Geometry$b[electronic resource] /$fby Nicola Gigli, Enrico Pasqualetto 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XI, 204 p. 8 illus.) 225 1 $aSISSA Springer Series,$x2524-857X ;$v2 311 $a3-030-38612-0 327 $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 ?ow on metric measure spaces -- 6. Second-order calculus on RCD spaces -- 7. Appendix A: Functional analytic tools -- 8. Appendix B: Solutions to the exercises. 330 $aThis book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces ? known as RCD spaces ? satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of ?infinitesimally Hilbertian? metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry. 410 0$aSISSA Springer Series,$x2524-857X ;$v2 606 $aDifferential geometry 606 $aCalculus 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aCalculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12220 615 0$aDifferential geometry. 615 0$aCalculus. 615 14$aDifferential Geometry. 615 24$aCalculus. 676 $a516.36 700 $aGigli$b Nicola$4aut$4http://id.loc.gov/vocabulary/relators/aut$0227784 702 $aPasqualetto$b Enrico$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418260603316 996 $aLectures on Nonsmooth Differential Geometry$92311004 997 $aUNISA