A User’s Guide to Optimal Transport

Luigi Ambrosio, Nicola Gigli

Type: Book-Chapter

Publication Date: 2012-09-04

Citations: 352

DOI: https://doi.org/10.1007/978-3-642-32160-3_1

View Publication

Download PDF

Locations

Lecture notes in mathematics - View
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Optimal Transport and Curvature	2011	Alessio Figalli Cédric Villani
+	Optimal Mass Transport on Euclidean Spaces	2023	Francesco Maggi
+	OPTIMAL TRANSPORTATION THEORY AND APPLICATIONS	2014	Filippo Santambrogio Amirali Fathi Yann Ollivier
+ PDF Chat	Introduction to optimal transport theory	2014	Filippo Santambrogio
+	Optimal Transport	2008	Cédric Villani
+	An Eulerian Approach to Optimal Transport with Applications to the Otto Calculus	2017	Benjamin Ira Schachter
+	Introduction to Optimal Mass Transport	2024	Olga Movilla Miangolarra
+	Arbeitsgemeinschaft: Optimal Transport and Geometry	2009	Félix Otto Karl‐Theodor Sturm
+	Optimal Transportation and Functional Inequalities	2013	Dominique Bakry Ivan Gentil Michel Ledoux
+ PDF Chat	Introduction to Optimal Transport Theory	2009	Filippo Santambrogio
+ PDF Chat	Introduction to Optimal Transport Theory	2009	Filippo Santambrogio
+	A Brief on Optimal Transport	2020	Austin Vandegriffe
+ PDF Chat	Book review: “Lectures on Optimal Transport” by Luigi Ambrosio, Elia Brué and Daniele Semola, and “An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows” by Alessio Figalli and Federico Glaudo	2022	Filippo Santambrogio
+	Optimal transportation, geometry and functional inequalities	2010	Luigi Ambrosio
+	Optimal Transport: Old and New	2013	Cédric Villani
+ PDF Chat	Lecture notes on gradient flows and optimal transport	2014	Sara Daneri Giuseppe Savaré
+	A general framework for multi-marginal optimal transport	2024	Brendan Pass Adolfo Vargas-Jiménez
+	Advances in Numerical Optimal Transportation	2015	Jean‐David Benamou
+	INTRODUCTION TO OPTIMAL TRANSPORTATION	2017	D. J. H. Garling
+	Calibrating optimal transportation: a new pseudo-Riemannian geometry	2009	Young‐Heon Kim Robert J. McCann Micah Warren

Works That Cite This (326)

Action	Title	Year	Authors
+ PDF Chat	Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes	2018	Valentina Masarotto Victor M. Panaretos Yoav Zemel
+	On quotients of spaces with Ricci curvature bounded below	2018	Fernando Galaz‐García Martin Kell Andrea Mondino Gerardo Sosa
+ PDF Chat	Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow	2017	Alessio Figalli Moon-Jin Kang Javier Morales
+	Higher order concentration for functions of weakly dependent random variables	2019	Friedrich Götze Holger Sambale Arthur Sinulis
+ PDF Chat	Martingale optimal transport duality	2020	Patrick Cheridito Matti Kiiski David J. Prömel H. Meté Soner
+ PDF Chat	Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes	2017	Gabriel Turinici
+ PDF Chat	Quasi-static damage evolution and homogenization: A case study of non-commutability	2014	Andrea Braides Biagio Cassano Adriana Garroni David Sarrocco
+ PDF Chat	Stratified spaces and synthetic Ricci curvature bounds	2021	Jérôme Bertrand C. Ketterer Ilaria Mondello Thomas Richard
+	A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles	2020	José A. Carrillo Matías G. Delgadino Grigorios A. Pavliotis
+ PDF Chat	Existence of Solutions to the Nonlinear Kantorovich Transportation Problem	2022	В. И. Богачев Ayrat Vladimirovich Rezbayev

Works Cited by This (73)

Action	Title	Year	Authors
+	A geometrical approach to monotone functions in $\mathbb R^n$	1999	Giovanni Alberti Luigi Ambrosio
+	Gradient Flows: In Metric Spaces and in the Space of Probability Measures	2005	Luigi Ambrosio Nicola Gigli Giuseppe Savaré
+ PDF Chat	Asymptotic Theory of Finite Dimensional Normed Spaces	1986	Vitali Milman Gideon Schechtman
+	Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs	2001	Luis Caffarelli Mikhail Feldman Robert J. McCann
+ PDF Chat	Topics in Optimal Transportation	2003	Cédric Villani
+	Geometric Problems in the Theory of Infinite-dimensional Probability Distributions	1979	V. N. Sudakov H. H. McFaden
+	A Course in Metric Geometry	2001	Dmitri Burago Yuri Burago S. V. Ivanov
+ PDF Chat	Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below—The Compact Case	2012	Luigi Ambrosio Nicola Gigli Giuseppe Savaré
+	On the Monge mass transfer problem	2001	Neil S. Trudinger Xu‐Jia Wang
+ PDF Chat	Ricci curvature for metric-measure spaces via optimal transport	2009	John Lott Cédric Villani