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Record Nr. |
UNISA996418260603316 |
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Autore |
Gigli Nicola |
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Titolo |
Lectures on Nonsmooth Differential Geometry [[electronic resource] /] / by Nicola Gigli, Enrico Pasqualetto |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
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ISBN |
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Edizione |
[1st ed. 2020.] |
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Descrizione fisica |
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1 online resource (XI, 204 p. 8 illus.) |
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Collana |
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SISSA Springer Series, , 2524-857X ; ; 2 |
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Disciplina |
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Soggetti |
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Differential geometry |
Calculus |
Differential Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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basic knowledge of functional analysis, measure theory, and Riemannian geometry. |
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