Lectures on Nonsmooth Differential Geometry

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Achat E-Book : Lectures on Nonsmooth Differential Geometry - Nicola Gigli - Enrico Pasqualetto
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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Lectures on Nonsmooth Differential Geometry

Lectures on Nonsmooth Differential Geometry

Nicola Gigli

Enrico Pasqualetto

Caractéristiques du produit :
E-Book
Référence : 9783030386139
Sortie le : 10/02/2020
Editeur : SPRINGER
Format : EPUB
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- Nicola Gigli  - Enrico Pasqualetto
Achat E-Book : Lectures on Nonsmooth Differential Geometry - Nicola Gigli - Enrico Pasqualetto

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