Uniform density theorem for the Hubbard model,
with Elliott H. Lieb and
J. Math. Phys 34, 891-898 (1993)
A Convexity Theory for Interacting Gases and Equilibrium Crystals.
PhD Thesis, Princeton University (1994)
Existence and uniqueness of monotone measure-preserving maps.
Duke Math. J. 80, 309-323, (1995)
Optimal maps in Monge's mass transport problem,
with Wilfrid Gangbo.
C.R. Acad. Sci. Paris. Ser. I. Math.
325, 1653-1658 (1995)
The geometry of optimal transportation, with Wilfrid
Acta Math. 177, 113-161 (1996)
A convexity principle for interacting gases.
Adv. Math. 128, 153-179 (1997)
Equilibrium shapes for planar crystals in an external field.
Comm. Math. Phys. 195, 699-723 (1998)
Exact solutions to the transportation problem on the line.
Proc. Royal Soc. London Ser. A 455, 1341-1380 (1999)
Shape recognition via Wasserstein distance, with Wilfrid
Quart. Appl. Math. 58, 705-737 (2000)
Polar factorization of maps on Riemannian manifolds.
Geom. Funct. Anal. 11 (2001) 589-608
A Riemannian interpolation inequality a la Borell,
Brascamp and Lieb,
Cordero-Erausquin and Michael Schmuckenschlaeger.
Invent. Math. 146 (2001) 219-257
Constructing optimal maps in Monge's transport problem as a limit of
strictly convex costs, with Luis A.
J. Amer. Math. Soc. 15 (2002) 1-26
Uniqueness and transport density in Monge's mass transportation problem
, with Mikhail Feldman.
Calc. Var. Partial Differential Equations. 15 (2002) 81-113
Monge's transport problem on a Riemannian manifold,
with Mikhail Feldman.
Trans. Amer. Math. Soc. 354 (2002) 1667-1697
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
Stable rotating binary stars and fluid in a tube.
Houston J. Math. 32 (2006) 603-632
Phase transitions and symmetry breaking in singular diffusion,
with Jochen Denzler.
Proc. Natl. Acad. Sci. USA 100 (2003) 6922-6925.
Exact semi-geostrophic flows in an elliptical ocean basin,
with Adam Oberman.
Appendix by Maxim Trokhimtchouk.
Nonlinearity 17 (2004) 1891-1922
A least action principle for steepest descent in a non-convex landscape
with Nassif Ghoussoub.
Contemp. Math. 362 (2004)
Fast diffusion to self-similarity: complete spectrum,
long time asymptotics, and numerology, with Jochen
Arch. Rational Mech. Anal. 175 (2005) 301-342
Contractions in the 2-Wasserstein length space and thermalization of
granular media , with Jose A.
Carrillo and Cedric
Arch. Rational Mech. Anal. 179 (2006) 217-263
 Prekopa-Leindler type inequalities on
Riemannian manifolds, Jacobi fields, and optimal transport ,
Cordero-Erausquin and Michael Schmuckenschlaeger.
Ann. Fac. Sci. Toulouse Math. (6) 15 (2006) 613-635.
 Sharp decay rates for the
fastest conservative diffusions, with Yong-Jung
C. R. Acad. Sci. Paris Ser. I Math. 341 (2005) 157-162
 Potential theory and optimal
convergence rates in fast nonlinear diffusion, with
J. Math. Pures Appl. 86 (2006) 42-67
 Second-order asymptotics for
the fast-diffusion equation , with Dejan
Int. Math. Res. Not. 24947 (2006) 1-22
 Free boundaries in optimal transport
and Monge-Ampere obstacle problems, with
Luis A. Caffarelli.
Ann. of Math. (2) 171 (2010) 673-730
 Nonlinear diffusion from a delocalized
source: affine self-similarity, time reversal, & nonradial focusing
geometries , with Jochen
Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 865-888
 Ricci flow, entropy, and optimal transportation , with Peter
(formely titled Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow) Amer. J. Math. 132 (2010) 711-730
 Constructing a relativistic heat flow by transport time steps , with Marjolaine Puel. Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 2539-2580.
 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.
 Optimal partition of a large labor force into working pairs, with Maxim Trokhimtchouk. Econom. Theory 42 (2010) 375-395.
 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
 Continuity, curvature, and the general covariance of optimal transportation , with Young-Heon Kim. J. Eur. Math. Soc. (JEMS)
12 (2010) 1009-1040
 Curvature and the continuity of optimal transport , (joint work with Young-Heon Kim). Oberwolfach Rep. 4 (2007) 2060-2062
 Explicit Yamabe flow of an asymmetric cigar , with Almut Burchard and Aaron Smith. Methods Appl. Anal. 15 (2008) 65-80
 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.
 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.
 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
 Pseudo-Riemannian geometry
calibrates optimal transportation, with Young-Heon
Kim and Micah Warren . Math. Res. Lett. 17 (2010) 1183-1197.
 The Ma-Trudinger-Wang curvature for natural mechanical actions, with Paul W.Y.
Calc. Var. Partial Differential Equations. 41 (2011) 285-299
 When is multidimensional screening a convex program?, with Alessio
J. Econom. Theory 146 (2011) 454-478.
 Regularity of optimal transport maps on multiple products of spheres,
Kim . J. Eur. Math. Soc. (JEMS) 15 (2013) 1131-1166.
 Hoelder continuity for optimal multivalued mappings, with Maria Sosio.
SIAM J. Math. Anal. 43 (2011) 1855-1871
 Rectifiability of optimal transportation plans, with Brendan
Pass and Micah
Canad. J. Math. 64 (2012) 924-934
 Unique equilibria and substitution effects in a stochastic model of the marriage market, with Colin Decker,
Elliott H. Lieb, and Benjamin K.
J. Econom. Theory 148 (2013) 778-792
 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.
 Hoelder continuity and injectivity of
optimal maps, with Alessio
Arch. Rational Mech. Anal. 209 (2013) 747-795
 On supporting hyperplanes to convex bodies, with Alessio
Methods Appl. Anal. 20 (2013) 261-272.
 Optimal transportation with capacity constraints, with Jonathan
Trans. Amer. Math. Soc. 367 (2015) 1501-1521.
 Becker meets Ricardo: Multisector matching
with communication and cognitive skills, with Xianwen
Shi , Aloyius
Siow and Ronald
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
 Higher order time asymptotics of fast
diffusion in Euclidean space (via dynamical systems methods)
, with Jochen
Mem. Amer. Math. Soc. 234 (2015) 1-94
 A glimpse into the differential
topology and geometry of optimal transport .
Discrete Contin. Dyn. Syst. 34 (2014) 1605-1621.
 Insights into capacity
constrained optimal transport, with Jonathan Korman.
Proc. Natl. Acad. Sci. USA, 110 (2013) 10064-10067.
 Dual potentials for capacity constrained
optimal transport, with Jonathan Korman and Christian Seis. Calc. Var. Partial Differential Equations 54 (2015) 573-584.
 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.
 The spectrum of a family
of fourth-order nonlinear diffusions near the global attractor, with
Comm. Partial Differential Equations. 40 (2015) 191-218.
 Long-time asymptotic expansions
for nonlinear diffusions in Euclidean space
, with Jochen
Contemp. Math. 656 (2016) 85-94.
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.
 Academic wages and pyramid schemes: a mathematical model, with Alice Erlinger, Xianwen
Shi , Aloyius
Siow and Ronald
J. Functional Analysis 269 (2015) 2709-2746.
 The intrinsic dynamics of optimal transport, with Ludovic
J. Ecole Polytechnique - Math. 3 (2016) 67-98.
 Multi- to one-dimensional optimal transport, with Pierre-Andre Chiappori and Brendan Pass.
Comm. Pure Appl. Math. 70 (2017) 2405-2444.
 Multidimensional matching: theory and empirics, with Pierre-Andre Chiappori and Brendan Pass.
 On concavity of the monopolist's
problem facing consumers with nonlinear price preferences, with Kelvin Shuangjian
Comm. Pure and Applied Math. 72(7) (2019) 1386-1423
 Free discontinuties in
optimal transport, with Jun
Arch. Rational Mech. Anal. 232 (2019) 1505-1541.
 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 doi.org/10.1017/S0956792518000578
 Optimal transportation between unequal dimensions, with Brendan Pass. arXiv:1805.11187v2. Arch. Rational Mech. Analysis 238 (2020) 1475-1520 doi.org/10.1007/s00205-020-01569-5
 Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity, arXiv1808.1536v2. Camb. J. Math. 8:3 (2020) 609-681.
 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.
 Isodiametry, variance, and regular simplices from particle interactions, with Tongseok Lim
Archive Rational Mech. Analysis 241 (2021) 553-576.
 Geometrical bounds for the variance and recentered moments, with Tongseok Lim arXiv:2001:11851. Math. Oper. Res. 47 (2022) 286-296.
 Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary, with Annegret
Ketterer, and Eric
arXiv:2005.07435. SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020),
131, 29 pages. (Special issue in honor of Gromov's 75th birthday)
 Independence of synthetic Curvature Dimension conditions on transport distance exponent, with Afiny
Colinet, and Flavia
Trans. Amer. Math. Soc. 374 (2021) 5877-5923. arXiv:2005.07435
 On Fejes Toth's conjectured maximizer for the sum of angles between lines, with Tongseok Lim, Appl. Math. Optim. 84(3) (2021) 3217-3227. DOI 10.1007/s00245-020-09745-5 arXiv:2007.08698
 Maximizing expected powers of the angle between pairs of points in projective space, with Tongseok Lim, to appear in Probab. Theory Related Fields, arXiv:2007.13052
 On the cardinality of sets in Rd obeying a slightly obtuse angle bound, with Tongseok Lim, SIAM J. Discrete Math, 36 (2022) 1093-1101, arXiv:2007.13871
 Classifying minimum energy states for interacting particles: spherical shells, with Cameron Davies and Tongseok Lim, SIAM J. Appl. Math. 82 (2022) 1520-1536. arXiv:2107.11718
 Classifying minimum energy states for interacting particles: regular simplices, with Cameron Davies and Tongseok Lim, to appear in Comm. Math. Phys. arXiv:2109.07091
 A Lorentzian analog for Hausdorff dimension and measure, with Clemens Saemann, to appear in Pure and Applied Analysis, arXiv:2110.04386
 Asymptotics near extinction for nonlinear fast diffusion on a bounded domain, with Beomjun Choi and Christian Seis, arXiv:2202.02769
 Villani's `Birth of a Theorem',
SIAM News 48 #10 (2015) p9.
Professor Robert J. McCann, FRSC
Department of Mathematics
University of Toronto
40 St George St Room 6290
Toronto, Ontario M5S 2E4
Office: (416) 978-4658
E-mail: mccann -at- math -dot- toronto -dot- edu
Office location: Room BA 6124
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