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Lectures on Nonsmooth Differential Geometry
Engelsk Paperback
Lectures on Nonsmooth Differential Geometry
Engelsk Paperback

573 kr
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Om denne bog

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.


Product detaljer
Sprog:
Engelsk
Sider:
204
ISBN-13:
9783030386153
Indbinding:
Paperback
Udgave:
ISBN-10:
3030386155
Udg. Dato:
11 feb 2021
Længde:
0mm
Bredde:
155mm
Højde:
235mm
Forlag:
Springer Nature Switzerland AG
Oplagsdato:
11 feb 2021
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