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Book
Gigli N, Ambrosio L, Savaré G. Gradient flows : in metric spaces and in the space of probability measures. Basel: Birkhäuser; 2005 pp. 1–333.
Gigli N, Pasqualetto E. Lectures on Nonsmooth Differential Geometry. Cham: Springer; 2020 pp. 1–204. Available from: https://books.sissa.it/libero/WebOpac.cls?VERSION=2&ACTION=DISPLAY&RSN=49974&DATA=DLS&TOKEN=rnz5TAi0pF7744&Z=1&SET=1
Book Chapter
Ambrosio L, Gigli N, Savaré G. Heat flow and calculus on metric measure spaces with ricci curvature bounded below—The compact case. In: Analysis and numerics of partial differential equations. Vol. 4. Analysis and numerics of partial differential equations. Milano: Springer Italia; 2013. pp. 63–115. Available from: http://www.springer.com/la/book/9788847025912
Ambrosio L, Gigli N. A user's guide to optimal transport. In: Modelling and Optimisation of Flows on Networks : Cetraro, Italy 2009. Vol. 2062. Modelling and Optimisation of Flows on Networks : Cetraro, Italy 2009. HEIDELBERG, DORDRECHT, LONDON: Springer-Verlag BERLIN-HEIDELBERG; 2013. pp. 1–155. Available from: https://link.springer.com/book/10.1007%2F978-3-642-32160-3
Journal Article
Brena C, Gigli N. About the general chain rule for functions of bounded variation. NONLINEAR ANALYSIS [Internet]. 2024 ;242:1–12. Available from: https://arxiv.org/abs/2307.06008
Gigli N, Mosconi S. The Abresch-Gromoll inequality in a non-smooth setting. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS [Internet]. 2014 ;34:1481–1509. Available from: https://arxiv.org/abs/1209.3813
Gigli N, Mosconi S. The abstract Lewy-Stampacchia inequality and applications. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES [Internet]. 2015 ;104:258–275. Available from: https://arxiv.org/abs/1401.4911
Esselborn E, Gigli N, Otto F. Algebraic contraction rate for distance between entropy solutions of scalar conservation laws. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS [Internet]. 2016 ;435:1525–1551. Available from: https://doi.org/10.1016/j.jmaa.2015.11.027
Ambrosio L, Gigli N, Savaré G. Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds. ANNALS OF PROBABILITY [Internet]. 2015 ;43:339–404. Available from: https://arxiv.org/abs/1209.5786
Gigli N, Pasqualetto E. Behaviour of the reference measure on RCD spaces under charts. COMMUNICATIONS IN ANALYSIS AND GEOMETRY. 2017 .
Gigli N, Tamanini L. Benamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces. Probability Theory and Related Fields [Internet]. 2019 . Available from: https://doi.org/10.1007/s00440-019-00909-1
Gigli N, Tamanini L. Benamou–Brenier and duality formulas for the entropic cost on RCD∗(K, N) spaces. PROBABILITY THEORY AND RELATED FIELDS [Internet]. 2020 ;176:1–34. Available from: https://arxiv.org/abs/1805.06325v1
Brena C, Gigli N. Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces. THE JOURNAL OF GEOMETRIC ANALYSIS [Internet]. 2024 ;34:1–54. Available from: https://arxiv.org/abs/2204.04174
Ambrosio L, Gigli N, Savaré G. Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below. INVENTIONES MATHEMATICAE [Internet]. 2014 ;195:289–391. Available from: https://arxiv.org/abs/1106.2090
Gigli N, Ambrosio L. Construction of the parallel transport in the Wasserstein space. METHODS AND APPLICATIONS OF ANALYSIS [Internet]. 2008 ;15:1–30. Available from: https://projecteuclid.org/euclid.maa/1228920869
Gigli N, Han BX. The continuity equation on metric measure spaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS [Internet]. 2015 ;53:149–177. Available from: https://arxiv.org/abs/1406.6350
Gigli N, Mondino A, Savaré G. Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY [Internet]. 2015 ;111:1071–1129. Available from: https://arxiv.org/abs/1311.4907
Ambrosio L, Gigli N, Savaré G. Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. REVISTA MATEMATICA IBEROAMERICANA [Internet]. 2013 ;29:969–996. Available from: https://arxiv.org/abs/1111.3730
Gigli N, Pasqualetto E, Soultanis E. Differential of metric valued Sobolev maps. JOURNAL OF FUNCTIONAL ANALYSIS [Internet]. 2020 ;278:1–18. Available from: https://arxiv.org/abs/1807.10063v1
Gigli N, Nobili F. A Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications. [Internet]. 2021 ;31(12):11780 - 11818. Available from: https://doi.org/10.1007/s12220-021-00701-5
Gigli N, Nobili F. A Differential Perspective on Gradient Flows on CAT(κ) -Spaces and Applications. THE JOURNAL OF GEOMETRIC ANALYSIS [Internet]. 2021 ;31:11780–11818. Available from: https://arxiv.org/abs/2012.12952
Gigli N, Pasqualetto E. Differential structure associated to axiomatic Sobolev spaces. Expositiones Mathematicae [Internet]. 2019 . Available from: http://www.sciencedirect.com/science/article/pii/S0723086918300975
Gigli N, Pasqualetto E. Differential structure associated to axiomatic Sobolev spaces. EXPOSITIONES MATHEMATICAE. 2019 ;38:480–495.
Gigli N. On the differential structure of metric measure spaces and applications. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY [Internet]. 2015 ;236:1–91. Available from: http://cvgmt.sns.it/paper/1800/
Ambrosio L, Gigli N, Savaré G. Diffusion, Optimal Transport and Ricci Curvature for Metric Measure Space. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY [Internet]. 2017 ;3:19–28. Available from: http://www.ems-ph.org/journals/show_abstract.php?issn=1027-488X&vol=3&iss=103&rank=4

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