(DOWNLOAD) "Lectures on Nonsmooth Differential Geometry" by Nicola Gigli & Enrico Pasqualetto " Book PDF Kindle ePub Free
eBook details
- Title: Lectures on Nonsmooth Differential Geometry
- Author : Nicola Gigli & Enrico Pasqualetto
- Release Date : January 10, 2020
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 9922 KB
Description
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.
 "Lectures on Nonsmooth Differential Geometry" by Nicola Gigli & Enrico Pasqualetto " Book PDF Kindle ePub Free){kind=link}