Lectures on Nonsmooth Differential Geometry (eBook)

Nicola Gigli, Enrico Pasqualetto (Autoren)

eBook Download: PDF

2020
204 Seiten
Springer International Publishing (Verlag)
978-3-030-38613-9 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 10.2.2020
• Reihe/Serie: SISSA Springer Series
• Reihe/Serie: SISSA Springer Series
• Zusatzinfo: XI, 204 p. 8 illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Differential Calculus • Differential Geometry • Geometric Ananlysis • Lower Ricci Curvature Bounds • nonsmooth calculus
• ISBN-10: 3-030-38613-9 / 3030386139
• ISBN-13: 978-3-030-38613-9 / 9783030386139