Partial regularity for optimal transport maps

Hölder Continuity and Injectivity of Optimal Maps

(2013) Alessio Figalli et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Regularity of optimal transport maps on multiple products of spheres

(2013) Alessio Figalli et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Positively Curved Riemannian Locally Symmetric Spaces are Positively Squared Distance Curved

(2012) Philippe Delanoë et al.   CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES

Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds

(2012) Alessio Figalli et al.   TOHOKU MATHEMATICAL JOURNAL

Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)

(2011) Young-Heon Kim et al.   JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna

(2010) Grégoire Loeper   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

On the Ma–Trudinger–Wang curvature on surfaces

(2010) Alessio Figalli et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Regularity Properties of Optimal Maps Between Nonconvex Domains in the Plane

(2010) Alessio Figalli   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Partial regularity of Brenier solutions of the Monge-Ampère equation

(2010) Alessio Figalli et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Local semiconvexity of Kantorovich potentials on non-compact manifolds

(2010) Alessio Figalli et al.   ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS

Optimal transportation on non-compact manifolds

(2010) Albert Fathi et al.   ISRAEL JOURNAL OF MATHEMATICS

On the regularity of solutions of optimal transportation problems

(2009) Grégoire Loeper   ACTA MATHEMATICA

C 1 regularity of solutions of the Monge–Ampère equation for optimal transport in dimension two

(2009) Alessio Figalli et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

InteriorC2,αRegularity for Potential Functions in Optimal Transportation

(2009) Jiakun Liu et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2

(2009) Alessio Figalli et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

On Strict Convexity and Continuous Differentiability of Potential Functions in Optimal Transportation

(2008) Neil S. Trudinger et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS