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  2. Regning og matematisk analyse
  3. Integralregning og integralligninger

Lectures on Nonsmooth Differential Geometry

Af: Nicola Gigli, Enrico Pasqualetto Engelsk Hardback

Lectures on Nonsmooth Differential Geometry

Af: Nicola Gigli, Enrico Pasqualetto Engelsk Hardback
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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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 204
ISBN-13: 9783030386122
Indbinding: Hardback
Udgave:
ISBN-10: 3030386120
Kategori: Integralregning og integralligninger
Udg. Dato: 11 feb 2020
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 11 feb 2020
Forfatter(e): Nicola Gigli, Enrico Pasqualetto
Forfatter(e) Nicola Gigli, Enrico Pasqualetto

Kategori Integralregning og integralligninger

ISBN-13 9783030386122

Sprog Engelsk

Indbinding Hardback

Sider 204

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 11 feb 2020

Oplagsdato 11 feb 2020

Forlag Springer Nature Switzerland AG

Kategori sammenhænge