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Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)

Proceedings of the International Congress of Mathematicians (ICM 2018), pp. 301-340 (2019) No AccessCALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACESLUIGI AMBROSIOLUIGI AMBROSIOSCUOLA NORMALE SUPERIORE, PIAZZA CAVALIERI 7, 56126, PISA, ITALYhttps://doi.org/10.1142/9789813272880_0015Cited by:12 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The theory of curvature-dimension bounds for nonsmooth spaces has several motivations: the study of functional and geometric inequalities in structures which arc very far from being Euclidean, therefore with new non-Riemannian tools, the description of the "closure" of classes of Riemannian manifolds under suitable geometric constraints, the stability of analytic and geometric properties of spaces (e.g. to prove rigidity results). Even though these goals may occasionally be in conflict, in the last few years we have seen spectacular developments in all these directions, and my text is meant both as a survey and as an introduction to this quickly developing research field. MSC2010: primary 30L99, secondary 53C21, secondary 49Q20, secondary 35K05 FiguresReferencesRelatedDetailsCited By 12Boundary regularity and stability for spaces with Ricci bounded belowElia Bruè, Aaron Naber and Daniele Semola11 February 2022 | Inventiones mathematicae, Vol. 228, No. 2Isotropic‐Nematic Phase Transition and Liquid Crystal DropletsFanghua Lin and Changyou Wang16 April 2022 | Communications on Pure and Applied Mathematics, Vol. 68Non-Hilbertian tangents to Hilbertian spacesDanka Lučić, Enrico Pasqualetto and Tapio Rajala5 April 2022 | Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 236Existence and Uniqueness of Green's Functions to Nonlinear Yamabe ProblemsYanyan Li and Luc Nguyen10 March 2022 | Communications on Pure and Applied Mathematics, Vol. 81On Clusters and the Multi-isoperimetric Profile in Riemannian Manifolds with Bounded GeometryReinaldo Resende de Oliveira8 March 2022 | Journal of Dynamical and Control Systems, Vol. 29Riemannian submersions for q-entropiesNikolaos Kalogeropoulos25 September 2021 | International Journal of Geometric Methods in Modern Physics, Vol. 18, No. 14Cheeger bounds on spin-two fieldsG. Bruno De Luca, Nicolò De Ponti, Andrea Mondino and Alessandro Tomasiello31 December 2021 | Journal of High Energy Physics, Vol. 2021, No. 12A Talenti-type comparison theorem for $${{\,\mathrm{RCD}\,}}(K,N)$$ spaces and applicationsAndrea Mondino and Mattia Vedovato14 July 2021 | Calculus of Variations and Partial Differential Equations, Vol. 60, No. 4Lecture 19: Heat Flow, Optimal Transport and Ricci CurvatureLuigi Ambrosio, Elia Brué and Daniele Semola23 July 2021Quasi-Continuous Vector Fields on RCD SpacesClément Debin, Nicola Gigli and Enrico Pasqualetto18 February 2020 | Potential Analysis, Vol. 54, No. 1Second-Order Calculus on RCD SpacesNicola Gigli and Enrico Pasqualetto11 February 2020Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD SpacesLuigi Ambrosio, Elia Brué and Daniele Semola1 July 2019 | Geometric and Functional Analysis, Vol. 29, No. 4 Proceedings of the International Congress of Mathematicians (ICM 2018)Metrics History PDF download

CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES