Publications of Robert J. McCann

[1] Uniform density theorem for the Hubbard model, with Elliott H. Lieb and Michael Loss. J. Math. Phys 34, 891-898 (1993)
[2] A Convexity Theory for Interacting Gases and Equilibrium Crystals. PhD Thesis, Princeton University (1994)
[3] Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80, 309-323, (1995)
[4] Optimal maps in Monge's mass transport problem, with Wilfrid Gangbo. C.R. Acad. Sci. Paris. Ser. I. Math. 325, 1653-1658 (1995)
[5] The geometry of optimal transportation, with Wilfrid Gangbo. Acta Math. 177, 113-161 (1996)
[6] A convexity principle for interacting gases. Adv. Math. 128, 153-179 (1997)
[7] Equilibrium shapes for planar crystals in an external field. Comm. Math. Phys. 195, 699-723 (1998)
[8] Exact solutions to the transportation problem on the line. Proc. Royal Soc. London Ser. A 455, 1341-1380 (1999)
[9] Shape recognition via Wasserstein distance, with Wilfrid Gangbo. Quart. Appl. Math. 58, 705-737 (2000)
[10] Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal. 11 (2001) 589-608
[11] A Riemannian interpolation inequality a la Borell, Brascamp and Lieb, with Dario Cordero-Erausquin and Michael Schmuckenschlaeger. Invent. Math. 146 (2001) 219-257
[12] Constructing optimal maps in Monge's transport problem as a limit of strictly convex costs, with Luis A. Caffarelli and Mikhail Feldman. J. Amer. Math. Soc. 15 (2002) 1-26
[13] Uniqueness and transport density in Monge's mass transportation problem , with Mikhail Feldman. Calc. Var. Partial Differential Equations. 15 (2002) 81-113
[14] Monge's transport problem on a Riemannian manifold, with Mikhail Feldman. Trans. Amer. Math. Soc. 354 (2002) 1667-1697
[15] Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, with Jose A. Carrillo and Cedric Villani. Revista Mat. Iberoamericana 19 (2003) 971-1018
[16] Stable rotating binary stars and fluid in a tube. Houston J. Math. 32 (2006) 603-632
[17] Phase transitions and symmetry breaking in singular diffusion, with Jochen Denzler. Proc. Natl. Acad. Sci. USA 100 (2003) 6922-6925.
[18] Exact semi-geostrophic flows in an elliptical ocean basin, with Adam Oberman. Appendix by Maxim Trokhimtchouk. Nonlinearity 17 (2004) 1891-1922
[19] A least action principle for steepest descent in a non-convex landscape , with Nassif Ghoussoub. Contemp. Math. 362 (2004) 177-187.
[20] Fast diffusion to self-similarity: complete spectrum, long time asymptotics, and numerology, with Jochen Denzler. Arch. Rational Mech. Anal. 175 (2005) 301-342
[21] Contractions in the 2-Wasserstein length space and thermalization of granular media , with Jose A. Carrillo and Cedric Villani. Arch. Rational Mech. Anal. 179 (2006) 217-263
[22] Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport , with Dario Cordero-Erausquin and Michael Schmuckenschlaeger. Ann. Fac. Sci. Toulouse Math. (6) 15 (2006) 613-635.
[23] Sharp decay rates for the fastest conservative diffusions, with Yong-Jung Kim. C. R. Acad. Sci. Paris Ser. I Math. 341 (2005) 157-162
[24] Potential theory and optimal convergence rates in fast nonlinear diffusion, with Yong-Jung Kim. J. Math. Pures Appl. 86 (2006) 42-67
[25] Second-order asymptotics for the fast-diffusion equation , with Dejan Slepcev. Int. Math. Res. Not. 24947 (2006) 1-22
[26] Free boundaries in optimal transport and Monge-Ampere obstacle problems, with Luis A. Caffarelli. Ann. of Math. (2) 171 (2010) 673-730
[27] Nonlinear diffusion from a delocalized source: affine self-similarity, time reversal, & nonradial focusing geometries , with Jochen Denzler. Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 865-888
[28] Ricci flow, entropy, and optimal transportation , with Peter Topping. (formely titled Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow) Amer. J. Math. 132 (2010) 711-730
[29] Constructing a relativistic heat flow by transport time steps , with Marjolaine Puel. Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 2539-2580.
[30] Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing , with Dorian Goldman. Nonlinearity 21 (2008) 1455-1470 doi 10.1088/0951-7715/21/7/005.
[31] Optimal partition of a large labor force into working pairs, with Maxim Trokhimtchouk. Econom. Theory 42 (2010) 375-395.
[32] Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness, with Pierre-Andre Chiappori and Lars Nesheim. Econom. Theory 42 (2010) 317-354
[33] Continuity, curvature, and the general covariance of optimal transportation , with Young-Heon Kim. J. Eur. Math. Soc. (JEMS) 12 (2010) 1009-1040
[34] Curvature and the continuity of optimal transport , (joint work with Young-Heon Kim). Oberwolfach Rep. 4 (2007) 2060-2062
[35] Explicit Yamabe flow of an asymmetric cigar , with Almut Burchard and Aaron Smith. Methods Appl. Anal. 15 (2008) 65-80
[36] Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular) , with Young-Heon Kim. J. Reine Angew. Math. 664 (2012) 1-27.
[37] A family of nonlinear fourth order equations of gradient flow type, with Daniel Matthes and Giuseppe Savare. Comm. Partial Differential Equations. 34 (2009) 1352-1397.
[38] Optimal transportation, topology and uniqueness (formerly titled Extremal doubly stochastic measures and optimal transportation), with Najma Ahmad and Hwa Kil Kim. Bull. Math. Sci. 1 (2011) 13-32
[39] Pseudo-Riemannian geometry calibrates optimal transportation, with Young-Heon Kim and Micah Warren . Math. Res. Lett. 17 (2010) 1183-1197.
[40] The Ma-Trudinger-Wang curvature for natural mechanical actions, with Paul W.Y. Lee . Calc. Var. Partial Differential Equations. 41 (2011) 285-299
[41] When is multidimensional screening a convex program?, with Alessio Figalli and Young-Heon Kim . J. Econom. Theory 146 (2011) 454-478.
[42] Regularity of optimal transport maps on multiple products of spheres, with Alessio Figalli and Young-Heon Kim . J. Eur. Math. Soc. (JEMS) 15 (2013) 1131-1166.
[43] Hoelder continuity for optimal multivalued mappings, with Maria Sosio. SIAM J. Math. Anal. 43 (2011) 1855-1871
[44] Rectifiability of optimal transportation plans, with Brendan Pass and Micah Warren . Canad. J. Math. 64 (2012) 924-934
[45] Unique equilibria and substitution effects in a stochastic model of the marriage market, with Colin Decker, Elliott H. Lieb, and Benjamin K. Stephens . J. Econom. Theory 148 (2013) 778-792
[46] Five lectures on optimal transportation: geometry, regularity and applications, with Nestor Guillen. In Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the Seminaire de Mathematiques Superieure (SMS) Montreal 2011. G. Dafni et al, eds. Providence: Amer. Math. Soc. (2013) 145-180.
[47] Hoelder continuity and injectivity of optimal maps, with Alessio Figalli and Young-Heon Kim . Arch. Rational Mech. Anal. 209 (2013) 747-795
[48] On supporting hyperplanes to convex bodies, with Alessio Figalli and Young-Heon Kim . Methods Appl. Anal. 20 (2013) 261-272.
[49] Optimal transportation with capacity constraints, with Jonathan Korman Trans. Amer. Math. Soc. 367 (2015) 1501-1521.
[50] Becker meets Ricardo: Multisector matching with communication and cognitive skills, with Xianwen Shi , Aloyius Siow and Ronald Wolthoff. Originally titled Becker meets Ricardo: multisector matching with social and cognitive skills. Journal of Law, Economics and Organization (2015) doi: 10.1093/jleo/ewv002
[51] Higher order time asymptotics of fast diffusion in Euclidean space (via dynamical systems methods) , with Jochen Denzler and Herbert Koch. Mem. Amer. Math. Soc. 234 (2015) 1-94
[52] A glimpse into the differential topology and geometry of optimal transport . Discrete Contin. Dyn. Syst. 34 (2014) 1605-1621.
[53] Insights into capacity constrained optimal transport, with Jonathan Korman. Proc. Natl. Acad. Sci. USA, 110 (2013) 10064-10067.
[54] Dual potentials for capacity constrained optimal transport, with Jonathan Korman and Christian Seis. Calc. Var. Partial Differential Equations 54 (2015) 573-584.
[55] An elementary approach to linear programming duality with application to capacity constrained transport, with Jonathan Korman and Christian Seis. J. Convex Anal. 22 (2015) 797-808.
[56] The spectrum of a family of fourth-order nonlinear diffusions near the global attractor, with Christian Seis. Comm. Partial Differential Equations. 40 (2015) 191-218.
[57] Long-time asymptotic expansions for nonlinear diffusions in Euclidean space , with Jochen Denzler and Herbert Koch. Contemp. Math. 656 (2016) 85-94.
[58] Academic wages, singularities, phase transitions and pyramid schemes , Proceedings of the International Congress of Mathematicians (Seoul 2014) S.Y. Jang et al, eds., vol III Invited Lectures, Seoul, Kyung Moon SA, 2014, pp 835-849.
[59] Academic wages and pyramid schemes: a mathematical model, with Alice Erlinger, Xianwen Shi , Aloyius Siow and Ronald Wolthoff. J. Functional Analysis 269 (2015) 2709-2746.
[60] The intrinsic dynamics of optimal transport, with Ludovic Rifford J. Ecole Polytechnique - Math. 3 (2016) 67-98.
[62] Multi- to one-dimensional optimal transport, with Pierre-Andre Chiappori and Brendan Pass. Comm. Pure Appl. Math. 70 (2017) 2405-2444.
[63] Multidimensional matching, with Pierre-Andre Chiappori and Brendan Pass.
[64] On concavity of the monopolist's problem facing consumers with nonlinear price preferences, with Kelvin Shuangjian Zhang . To appear in Comm. Pure and Applied Math.
[65] Free discontinuties in optimal transport, with Jun Kitagawa. To appear in Arch. Rational Mech. Anal. DOI 10.1007/s00205-018-01348-3
[66] Transition to nestedness in multi- to one-dimensional optimal transport, with Pierre-Andre Chiappori and Brendan Pass.
[67] Optimal transport between unequal dimensions, with Brendan Pass.
[68] Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity, arXiv1808.1536v2.
[69] Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds, with Yik Chau (Kry) Lui, Gavin Weiguang Ding, and Ruitong Huang. To appear in NeurIPS (Neural Information Processing Systems) 2018.

[61] Villani's `Birth of a Theorem', SIAM News 48 #10 (2015) p9.

Professor Robert J. McCann
Department of Mathematics
University of Toronto Bahen Centre
40 St George St Room 6290
Toronto, Ontario M5S 2E4
Office: (416) 978-4658
FAX: 978-4107
E-mail: mccann -at- math -dot- toronto -dot- edu
Office location: Room BA 6124

Last modified on Thursday March 7, 2013
Comments and questions to mccann -at- math -dot- toronto -dot- edu @