Lectures on Nonsmooth Differential Geometry / / by Nicola Gigli, Enrico Pasqualetto

• Autore: Gigli Nicola
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
• Edizione: 1st ed. 2020.
• Descrizione fisica: 1 online resource (XI, 204 p. 8 illus.)
• Disciplina: 516.36
• Soggetto topico: Differential geometry; Calculus; Differential Geometry
• Persona (resp. second.): PasqualettoEnrico
• Nota di contenuto: 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.
• 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.
• Titolo autorizzato: Lectures on Nonsmooth Differential Geometry
• ISBN: 3-030-38613-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910483102803321
• Lo trovi qui: Univ. Federico II
• Serie: SISSA Springer Series, . 2524-857X ; ; 2