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 31 (4) (2015) 690-720 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: theory and empirics, 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. Comm. Pure and Applied Math. 72(7) (2019) 1386-1423
[65] Free discontinuties in optimal transport, with Jun Kitagawa. Arch. Rational Mech. Anal. 232 (2019) 1505-1541. 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. Euro. J. Appl. Math. 30 (2019) 1220-1228
[67] Optimal transportation between unequal dimensions, with Brendan Pass. arXiv:1805.11187v2. Arch. Rational Mech. Analysis 238 (2020) 1475-1520
[68] Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity, arXiv1808.1536v2. Camb. J. Math. 8:3 (2020) 609-681.
[69] Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds, with Yik Chau (Kry) Lui, Gavin Weiguang Ding, and Ruitong Huang. In Advances in Neural Information Processing Systems 31 (NeurIPS) S. Bengio et al, eds. Curran Associates Inc. 2018, pp 8453-8463.
[70] Isodiametry, variance, and regular simplices from particle interactions, with Tongseok Lim arXiv:1907.13593. To appear in Archive Rational Mech. Analysis
[71] Geometrical bounds for the variance and recentered moments, with Tongseok Lim arXiv:2001:11851. To appear in Math. Oper. Res.
[72] Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary, with Annegret Burtscher, Christian Ketterer, and Eric Woolgar, arXiv:2005.07435. SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020), 131, 29 pages. (Special issue in honor of Gromov's 75th birthday)
[73] Independence of synthetic Curvature Dimension conditions on transport distance exponent, with Afiny Akdemir, Fabio Cavalletti, Andrew Colinet, and Flavia Santarcangelo, to appear in Trans. Amer. Math. Soc. arXiv:2005.07435
[74] On Fejes Toth's conjectured maximizer for the sum of angles between lines, with Tongseok Lim, to appear in Appl. Math. Optim. arXiv:2007.08698
[75] Maximizing powers of the angle between pairs of points in projective space, with Tongseok Lim, arXiv:2007.13052
[76] On the cardinality of sets in Rd obeying a slightly obtuse angle bound, with Tongseok Lim, arXiv:2007.13871

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

Professor Robert J. McCann, FRSC
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 June 20, 2019
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