Lectures on Nonsmooth Differential Geometry

Released on by Nicola Gigli
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  • Lectures on Nonsmooth Differential Geometry Book Detail

  • Author : Nicola Gigli
  • Release Date : 2020-02-10
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 212
  • ISBN 13 : 3030386139
  • File Size : 40,40 MB
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Lectures on Nonsmooth Differential Geometry by Nicola Gigli PDF Summary

Book 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.

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