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. To appear in J. Reine Angew. Math.
[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 .
[42] Hoelder continuity and injectivity of
optimal maps, with Alessio
Figalli
and Young-Heon
Kim .
[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 . To appear
in Canad. J. Math.
[45] Regularity of optimal transport maps on multiple products of spheres,
with Alessio
Figalli
and Young-Heon
Kim . To appear in J. Eur. Math. Soc. (JEMS)
[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.
[48] On supporting hyperplanes to convex bodies, with Alessio
Figalli
and Young-Heon
Kim .
[49] Optimal transportation with capacity constraints, with Jonathan
Korman .
[50] Becker meets Ricardo: multisector matching
with social and cognitive skills, with Xianwen
Shi , Aloyius
Siow and Ronald
Wolthoff .
[51] Higher order time asymptotics of fast
diffusion in Euclidean space (via dynamical systems methods)
, with Jochen
Denzler and
Herbert Koch.
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
Monday October 25, 2010
Comments and questions to mccann -at- math -dot- toronto -dot- edu