bokomslag Lectures on Nonsmooth Differential Geometry
Vetenskap & teknik

Lectures on Nonsmooth Differential Geometry

Nicola Gigli Enrico Pasqualetto

Inbunden

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Andra format:

  • 204 sidor
  • 2020
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.
  • Författare: Nicola Gigli, Enrico Pasqualetto
  • Format: Inbunden
  • ISBN: 9783030386122
  • Språk: Engelska
  • Antal sidor: 204
  • Utgivningsdatum: 2020-02-11
  • Förlag: Springer Nature Switzerland AG