Geodesic
Partial regularity for optimal transport maps
De Philippis, Guido1  ; Figalli, Alessio2 
1 Scuola Normale Superiore p.za dei Cavalieri 7 56126 Pisa Italy
2 Department of Mathematics, The University of Texas at Austin 1 University Station C1200 78712 Austin TX USA
Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 81-112

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We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

DOI : 10.1007/s10240-014-0064-7
Keywords: Riemannian Manifold, Partial Regularity, Optimal Transport, Optimal Transportation, Smooth Density

De Philippis, Guido 1 ; Figalli, Alessio 2

1 Scuola Normale Superiore p.za dei Cavalieri 7 56126 Pisa Italy
2 Department of Mathematics, The University of Texas at Austin 1 University Station C1200 78712 Austin TX USA 
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     title = {Partial regularity for optimal transport maps},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {81--112},
     publisher = {Springer Berlin Heidelberg},
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     year = {2015},
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De Philippis, Guido; Figalli, Alessio. Partial regularity for optimal transport maps. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 81-112. doi: 10.1007/s10240-014-0064-7

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