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Lectures on Nonsmooth Differential G...
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Lectures on Nonsmooth Differential Geometry
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Lectures on Nonsmooth Differential Geometry/ by Nicola Gigli, Enrico Pasqualetto.
作者:
Gigli, Nicola.
其他作者:
Pasqualetto, Enrico.
面頁冊數:
XI, 204 p. 8 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Differential Geometry. -
電子資源:
https://doi.org/10.1007/978-3-030-38613-9
ISBN:
9783030386139
Lectures on Nonsmooth Differential Geometry
Gigli, Nicola.
Lectures on Nonsmooth Differential Geometry
[electronic resource] /by Nicola Gigli, Enrico Pasqualetto. - 1st ed. 2020. - XI, 204 p. 8 illus.online resource. - SISSA Springer Series,22524-857X ;. - SISSA Springer Series,1.
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.
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.
ISBN: 9783030386139
Standard No.: 10.1007/978-3-030-38613-9doiSubjects--Topical Terms:
671118
Differential Geometry.
LC Class. No.: QA641-670
Dewey Class. No.: 516.36
Lectures on Nonsmooth Differential Geometry
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