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 mod...
قائمة المحتويات
1. Preliminaries.- 2. Sobolev calculus on metric measure spaces.- 3. The theory of normed modules.- 4. First-order calculus on metric measure spaces.- 5. Heat flow ...
عن المؤلف
Nicola Gigli studied Mathematics at the Scuola Normale Superiore of Pisa and is Professor of Mathematical Analysis at SISSA, Trieste. He is interested in calculus of varia...