| 书目名称 | Lectures on Nonsmooth Differential Geometry |
| 编辑 | Nicola Gigli,Enrico Pasqualetto |
| 视频video | |
| 概述 | Provides a fairly self-contained introduction to the field.Offers content highly relevant to current research trends.Includes numerous exercises, with solutions |
| 丛书名称 | SISSA Springer Series |
| 图书封面 |  |
| 描述 | .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.. |
| 出版日期 | Book 2020 |
| 关键词 | Geometric Ananlysis; Nonsmooth Calculus; Lower Ricci Curvature Bounds; Differential Geometry; Differenti |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-38613-9 |
| isbn_softcover | 978-3-030-38615-3 |
| isbn_ebook | 978-3-030-38613-9Series ISSN 2524-857X Series E-ISSN 2524-8588 |
| issn_series | 2524-857X |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:24:01
