** Publications: **

[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
Mattes 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. and Partial Differential Equations.* **41** (2011) 285-299

[41] * 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

[42] * Hoelder continuity and injectivity of
optimal maps*, with Alessio
Figalli
and Young-Heon
Kim .
* Arch. Rational Mech. Anal.* ** 209 ** (2013) 747-795

[43] * When is multidimensional screening a convex program?*, with Alessio
Figalli
and Young-Heon
Kim .
*J. Econom. Theory* **146** (2011) 454-478.

[44] * Rectifiability of optimal transportation plans*, with Brendan
Pass and Micah
Warren .
*Canad. J. Math.* ** 64 ** (2012) 924-934

[45] * 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.

[46] * Hoelder continuity for optimal multivalued mappings, * with Maria Sosio. *
SIAM J. Math. Anal.* ** 43 ** (2011) 1855-1871

[47] * 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.

[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
To appear in * Trans. Amer. Math. Soc.*.

[50] * The organization of the labor market
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*.

[51] * Higher order time asymptotics of fast
diffusion in Euclidean space (via dynamical systems methods)
, * with Jochen
Denzler and
Herbert Koch.
To appear in * Mem. Amer. Math. Soc.*

[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.

[55] * A penalization approach to linear programming duality with application to capacity constrained transport, * with Jonathan Korman and Christian Seis.

[56] * The spectrum of a family
of fourth-order equations near the global attractor, * with
Christian Seis.

[57] * Long-time asymptotic expansions
for nonlinear diffusions in Euclidean space
, * with Jochen
Denzler and
Herbert Koch.
Proceedings of the 2013 Mathematical Congress of the Americas at Guanajuato (submitted)

[58] *
Academic wages, singularities, phase transitions and pyramid schemes
, *
Proceedings of the 2014 International Congress of Mathematics at Seoul (submitted)

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*
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