{"product_id":"lectures-on-nonsmooth-differential-geometry-9783030386139","title":"Lectures on Nonsmooth Differential Geometry","description":"\u003cp\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 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.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914847252759,"sku":null,"price":7422.41,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030386139.jpg?v=1781510685","url":"https:\/\/payment.letskitaboo.com\/te\/products\/lectures-on-nonsmooth-differential-geometry-9783030386139","provider":"Kitaboo One eStore","version":"1.0","type":"link"}