{"product_id":"lectures-on-nonsmooth-differential-geometry-nicola-gigli-9783030386122","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\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Nicola Gigli, Enrico Pasqualetto\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3030386120\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783030386122\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/11\/2020\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 204\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.07lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.56d","brand":"Nicola Gigli","offers":[{"title":"Hardcover","offer_id":43941641355519,"sku":"9783030386122","price":99.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_f0bf67fb-0231-4e65-8cf2-0435c99a300d.jpg?v=1681454108","url":"https:\/\/www.whiterainbookhouse.com\/products\/lectures-on-nonsmooth-differential-geometry-nicola-gigli-9783030386122","provider":"WR Book House","version":"1.0","type":"link"}