Lectures on Nonsmooth Differential Geometry / / by Nicola Gigli, Enrico Pasqualetto
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| Autore: |
Gigli Nicola
|
| Titolo: |
Lectures on Nonsmooth Differential Geometry / / by Nicola Gigli, Enrico Pasqualetto
|
| 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: | Geometry, Differential |
| 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 |
| Opac: | Controlla la disponibilità qui |
Serie:
SISSA Springer Series, . 2524-857X ; ; 2