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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 acomprehensive 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.
| Autorius: | Enrico Pasqualetto, Nicola Gigli, |
| Serija: | SISSA Springer Series |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2020 |
| Knygos puslapių skaičius: | 216 |
| ISBN-10: | 3030386120 |
| ISBN-13: | 9783030386122 |
| Formatas: | 241 x 160 x 18 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Lectures on Nonsmooth Differential Geometry“
