{"product_id":"lectures-on-nonsmooth-differential-geometry-9783030386153","title":"Lectures on Nonsmooth Differential Geometry","description":"\u003cp\u003e • Author(s): Nicola Gigli\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003eThis 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45279456886935,"sku":"9783030386153","price":4730.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783030386153.webp?v=1769293632","url":"https:\/\/atlanticbooks.com\/products\/lectures-on-nonsmooth-differential-geometry-9783030386153","provider":"Atlantic Books","version":"1.0","type":"link"}