Lectures on Nonsmooth Differential Geometry is popular PDF and ePub book, written by Nicola Gigli in 2020-02-10, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lectures on Nonsmooth Differential Geometry can be Read Online from any device for your convenience.
Lectures on Nonsmooth Differential Geometry Book PDF Summary
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.
Detail Book of Lectures on Nonsmooth Differential Geometry PDF
- Author : Nicola Gigli
- Release : 10 February 2020
- Publisher : Springer Nature
- ISBN : 9783030386139
- Genre : Mathematics
- Total Page : 212 pages
- Language : English
- PDF File Size : 12,7 Mb
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