Fetching the paper…
Reading the bibliography…
Let $X$ and $Y$ be domains of $\mathbb{R}^n$ equipped with respective probability measures $\mu$ and $ \nu$.
1903
Earlier work this paper cites.
Hawley, N. (1953). Constant holomorphic curvature. Canadian Journal of Mathematics, 5, 53-56. doi:10.4153/CJM-1953-007-1
1953
Earlier work this paper cites.
Kantorovitch, L. (1958). On the translocation of masses. Management Science, 5(1), 1-4
1958
Earlier work this paper cites.
Dombrowski, P. (1962). On the geometry of the tangent bundle. Journal für Mathematik. Bd, 210(1/2), 10
1962
Earlier work this paper cites.
Bregman, L. M. (1967). The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR computational mathematics and mathematical physics, 7(3), 200-217
1967
Earlier work this paper cites.
Mori, S. (1979). Projective manifolds with ample tangent bundles. Annals of Mathematics, 110(3), 593-606
1979
Earlier work this paper cites.
Siu, Y. T., & Yau, S. T. (1980). Compact Kähler manifolds of positive bisectional curvature. Inventiones mathematicae, 59(2), 189-204
1980
Earlier work this paper cites.
Brenier, Y. (1987) Décomposition polaire et réarrangement monotone des champs de vecteurs. C.R. Acad. Sci. Paris Sér. I Math., 305, 805–808
1987
Earlier work this paper cites.
Caffarelli, L. A. (1992). The regularity of mappings with a convex potential. Journal of the American Mathematical Society, 5(1), 99-104
1992
Earlier work this paper cites.
Yau, S. T. (1994) Open problems in geometry, Lectures on Differential Geometry, by Schoen and Yau 1, 365-404
1994
Earlier work this paper cites.
Gangbo, W., & McCann, R. J. (1995). Optimal maps in Monge’s mass transport problem. Comptes Rendus de l’Academie des Sciences-Serie I-Mathematique, 321(12), 1653
1995
Earlier work this paper cites.
Gangbo, W., & McCann, R. J. (1996). The geometry of optimal transportation. Acta Mathematica, 177(2), 113-161
1996
Earlier work this paper cites.
Wang, X. J. (2004). On the design of a reflector antenna II. Calculus of Variations and Partial Differential Equations, 20(3), 329-341
2004
Earlier work this paper cites.
Zhang, J. (2004). Divergence function, duality, and convex analysis. Neural Computation, 16(1), 159-195
2004
Earlier work this paper cites.
Ma, X. N., Trudinger, N. S., & Wang, X. J. (2005). Regularity of potential functions of the optimal transportation problem. Archive for rational mechanics and analysis, 177(2), 151-183
2005
Earlier work this paper cites.
Chen, X. X. (2007). On Kähler manifolds with positive orthogonal bisectional curvature. Advances in Mathematics, 215(2), 427-445
2007
Earlier work this paper cites.
Satoh, H. (2007). Almost Hermitian structures on tangent bundles. In Proceedings of The Eleventh International Workshop on Differential. Geometry, Kyungpook Nat. Univ., Taegu (Vol. 11, pp. 105-118)
2007
Cited alongside, same era.
Shima, H. (2007). Geometry of Hessian Structures. World Scientific Publishing Co. Singapore
2007
Cited alongside, same era.
Villani, C. (2008). Optimal transport: old and new (Vol. 338). Springer Science & Business Media
2008
Cited alongside, same era.
Loeper, G. (2009). On the regularity of solutions of optimal transportation problems. Acta mathematica, 202(2), 241-283
2009
Cited alongside, same era.
Seshadri, H. (2009). Manifolds with nonnegative isotropic curvature. Communications in Analysis and Geometry, 17(4), 621-635
2009
Cited alongside, same era.
Molitor, M. (2014). Gaussian distributions, Jacobi group, and Siegel-Jacobi space. Journal of Mathematical Physics, 55(12), 122102
2014
Later among the works it cites.
Amari, S. I. (2016). Information geometry and its applications (Vol. 194). Tokyo: Springer
2016
Later among the works it cites.
Pal, S., & Wong, T. K. L. (2016). The geometry of relative arbitrage. Mathematics and Financial Economics, 10(3), 263-293
2016
Later among the works it cites.
Feng, H., Liu, K., & Wan, X. (2017). Compact Kähler manifolds with positive orthogonal bisectional curvature. Mathematical Research Letters, 24(3), 767-780
2017
Later among the works it cites.
Gentil, I., Léonard, C., & Ripani, L. (2017). About the analogy between optimal transport and minimal entropy. Ann. Fac. Toulouse, Série 6, Vol.26 (3), 569-600
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Trudinger, N. S., & Wang, X. J. (2009). On the second boundary value problem for Monge-Ampere type equations and optimal transportation. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze-Serie IV, 8(1), 143
2009
Cited alongside, same era.
Gu, H., & Zhang, Z. (2010). An extension of Mok’s theorem on the generalized Frankel conjecture. Science China Mathematics, 53(5), 1253-1264
2010
Cited alongside, same era.
Kim, Y. H., & McCann, R. J. (2010). Continuity, curvature, and the general covariance of optimal transportation. Journal of the European Mathematical Society, 12(4), 1009-1040
2010
Cited alongside, same era.
Kim, Y. H., McCann, R. J., & Warren, M. (2010). Pseudo-Riemannian geometry calibrates optimal transportation. Mathematical Research Letters, 17(6), 1183-1197
2010
Cited alongside, same era.
Wu, H.H. & Zheng F. (2010). Examples of positively curved complete Kähler manifolds, Geometry and Analysis Volume I, Advanced Lecture in Mathematics 17, Higher Education Press and International Press, Beijing and Boston, pp. 517–542
2010
Cited alongside, same era.
Figalli, A., Kim, Y. H., & McCann, R. J. (2011). When is multidimensional screening a convex program?. Journal of Economic Theory, 146(2), 454-478
2011
Cited alongside, same era.
2012
Cited alongside, same era.
Wong, T. K. L. (2017). On portfolios generated by optimal transport. arXiv preprint arXiv:1709.03169
2017
Later among the works it cites.
Khan G. (2018). MTW Notebook. Mathematica notebook. Available at https://sites.google.com/a/umich.edu/gabekhan/code/optimaltransport
2018
Closest in time.
Ni, L., & Zheng, F. (2018). Comparison and vanishing theorems for Kähler manifolds. Calculus of Variations and Partial Differential Equations, 57(6), 151
2018
Closest in time.
Pal, S., & Wong, T. K. L. (2018). Exponentially concave functions and a new information geometry. The Annals of Probability, 46(2), 1070-1113
2018
Closest in time.
2018
Closest in time.
Wong, T. K. L. (2018). Logarithmic divergences from optimal transport and Rényi geometry. Information Geometry, 1(1), 39-78
2018
Closest in time.
Khan, G., & Zhang, J. (2019). Hessian curvature and optimal transport. To appear in Geometric Science of Information, GSI2019
2019
Closest in time.
Liu, G. (2019). On Yau’s uniformization conjecture. Cambridge Journal of Mathematics, 7(1), 33-70
2019
Closest in time.
Ni, L., & Niu, Y. (2019). Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature. Journal für die reine und angewandte Mathematik (Crelles Journal)
2019
Closest in time.
Peyré, G., & Cuturi, M. (2019). Computational optimal transport. Foundations and Trends ®
2019
Closest in time.