Some nonlinear problems in Riemannian geometry, 1998. ,
DOI : 10.1007/978-3-662-13006-3
Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas, 1978. ,
Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris Sér. I Math, vol.305, pp.805-808, 1987. ,
Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991. ,
DOI : 10.1002/cpa.3160440402
Nondivergent elliptic equations on manifolds with nonnegative curvature, Communications on Pure and Applied Mathematics, vol.50, issue.7, pp.623-665, 1997. ,
DOI : 10.1002/(SICI)1097-0312(199707)50:7<623::AID-CPA2>3.3.CO;2-B
Leçons sur la géométrie des espaces de Riemann, 1951. ,
Calcul différentiel, 1967. ,
Comparison theorems in Riemannian geometry, 2008. ,
DOI : 10.1090/chel/365
A Riemannian interpolation inequality ?? la Borell, Brascamp and Lieb, Inventiones Mathematicae, vol.146, issue.2, pp.219-257, 2001. ,
DOI : 10.1007/s002220100160
URL : https://hal.archives-ouvertes.fr/hal-00693677
Minimum and conjugate points in symmetric spaces, Journal canadien de math??matiques, vol.14, issue.0, pp.320-328, 1962. ,
DOI : 10.4153/CJM-1962-024-8
??quations du type de Monge???Amp??re sur les vari??t??s Riemanniennes compactes, II, Del82] Philippe Delanoë. ´ Equations du type de Monge?Ampère sur les variétés riemanniennes compactes, pp.341-353403, 1981. ,
DOI : 10.1016/0022-1236(81)90080-X
Local solvability of elliptic, and curvature, equations on compact manifolds, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2003, issue.558, pp.23-45, 2003. ,
DOI : 10.1515/crll.2003.041
Gradient rearrangement for diffeomorphisms of a compact manifold, Differential Geometry and its Applications, vol.20, issue.2, pp.145-165, 2004. ,
DOI : 10.1016/j.difgeo.2003.10.003
Regularity of optimal transport on compact, locally nearly spherical, manifolds, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2010, issue.646, pp.65-115, 2010. ,
DOI : 10.1515/crelle.2010.066
Locally nearly spherical surfaces are almost-positively $c$-curved, Methods and Applications of Analysis, vol.18, issue.3, pp.269-302, 2011. ,
DOI : 10.4310/MAA.2011.v18.n3.a2
Gradient estimates for potentials of invertible gradient???mappings on the sphere, Calculus of Variations and Partial Differential Equations, vol.487, issue.3, pp.297-311, 2006. ,
DOI : 10.1007/s00526-006-0006-4
Positively curved riemannian locally symmetric spaces are positively squared distance curved. Canad, J. Math, vol.65, issue.4, pp.757-767, 2013. ,
Classical solutions of fully nonlinear, convex , second-order elliptic equations, Comm. Pure Appl. Math, vol.35, issue.3, pp.333-363, 1982. ,
H??lder Continuity and Injectivity of Optimal Maps, Archive for Rational Mechanics and Analysis, vol.12, issue.3, pp.747-795, 2013. ,
DOI : 10.1007/s00205-013-0629-5
Regularity of optimal transport maps on multiple products of spheres, Journal of the European Mathematical Society, vol.15, issue.4, pp.1131-1166, 2013. ,
DOI : 10.4171/JEMS/388
On the Ma???Trudinger???Wang curvature on surfaces, Calculus of Variations and Partial Differential Equations, vol.255, issue.9, pp.3-4307, 2010. ,
DOI : 10.1007/s00526-010-0311-9
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds, Tohoku Mathematical Journal, vol.63, issue.4, pp.855-876, 2011. ,
DOI : 10.2748/tmj/1325886291
URL : https://hal.archives-ouvertes.fr/hal-00923320
Nearly Round Spheres Look Convex, American Journal of Mathematics, vol.134, issue.1, pp.109-139, 2012. ,
DOI : 10.1353/ajm.2012.0000
URL : https://hal.archives-ouvertes.fr/hal-00923321
Sur diff??rentes questions relatives aux ??quations du type elliptique, Annales scientifiques de l'??cole normale sup??rieure, vol.47, issue.221, pp.197-266, 1930. ,
DOI : 10.24033/asens.801
Elliptic partial differential equations of second order, Classics in Mathematics, 2001. ,
Ordinary differential equations Corrected reprint of the second (1982) edition, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.38, p.658490, 2002. ,
Elementare BemerkungenüberBemerkungen¨Bemerkungenüber die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Sitz. Ber. Preuss. Akad. Wissensch. Berlin, Math.? Phys. Kl, vol.19, pp.147-152, 1927. ,
???ber den funktionalen, insbesondere den analytischen Charakter der L???sungen elliptischer Differentialgleichungen zweiter Ordnung, Mathematische Zeitschrift, vol.34, issue.1, pp.194-233, 1931. ,
DOI : 10.1007/BF01180586
Riemannian geometry and geometric analysis, 2011. ,
DOI : 10.1007/978-3-642-21298-7
A geometric classification of positively curved symmetric spaces and the isoparametric construction of the Cayley plane On the geometry of differentiable manifolds, Astérisque, pp.163-164111, 1986. ,
Counterexamples to Continuity of Optimal Transport Maps on Positively Curved Riemannian Manifolds, International Mathematics Research Notices, vol.15, 2008. ,
DOI : 10.1093/imrn/rnn120
Riemannian geometry, 1995. ,
Continuity, curvature, and the general covariance of optimal transportation, J. Eur. Math. Soc. (JEMS), vol.12, issue.4, pp.1009-1040, 2010. ,
Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular), J. Reine Angew. Math, vol.664, pp.1-27, 2012. ,
Foundations of differential geometry. Vol. I. Wiley Classics Library, 1996. ,
Foundations of differential geometry Wiley Classics Library, 1996. ,
Introduction to differentiable manifolds. Universitext, 2002. ,
On the regularity of solutions of optimal transportation problems, Acta Mathematica, vol.202, issue.2, pp.241-283, 2009. ,
DOI : 10.1007/s11511-009-0037-8
Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna, Archive for Rational Mechanics and Analysis, vol.20, issue.3, pp.269-289, 2011. ,
DOI : 10.1007/s00205-010-0330-x
Regularity for Potential Functions in Optimal Transportation, Communications in Partial Differential Equations, vol.46, issue.1, pp.165-184, 2010. ,
DOI : 10.1007/s11401-006-0142-3
Regularity of optimal transport in curved geometry: The nonfocal case, Duke Mathematical Journal, vol.151, issue.3, pp.431-485, 2010. ,
DOI : 10.1215/00127094-2010-003
Polar factorization of maps on Riemannian manifolds, Geometric and Functional Analysis, vol.11, issue.3, pp.589-608, 2001. ,
DOI : 10.1007/PL00001679
Topology from the differentiable viewpoint Princeton Landmarks in Mathematics, 1997. ,
Mémoire sur la théorie des déblais et remblais, Mémoires Acad. Royale Sci. Paris, p.1781 ,
Regularity of potential functions of the optimal transportation problem, Arch. Ration. Mech. Anal, vol.177, issue.2, pp.151-183, 2005. ,
topology. I. Simply connected surfaces, Duke Mathematical Journal, vol.1, issue.3, pp.376-391, 1935. ,
DOI : 10.1215/S0012-7094-35-00126-0
Critical point theory and submanifold geometry, Lecture Notes in Mathematics, vol.1353, 1988. ,
Maximum principles in differential equations, N.J, 1967. ,
Fully nonlinear, uniformly elliptic equations under natural structure conditions, Trans. Amer. Math. Soc, vol.278, issue.2, pp.751-769, 1983. ,
On the second boundary value problem for Monge?Ampère type equations and optimal transportation, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.8, issue.51, pp.143-174, 2009. ,
Continuity and injectivity of optimal maps, Calculus of Variations and Partial Differential Equations, vol.20, issue.3, 2011. ,
DOI : 10.1007/s00526-014-0725-x
The Cut Locus and Conjugate Locus of a Riemannian Manifold, The Annals of Mathematics, vol.87, issue.1, pp.29-41, 1968. ,
DOI : 10.2307/1970592
Tangent and cotangent bundles: differential geometry, Pure and Applied Mathematics, issue.16, 1973. ,