[1] Otto F, Villani C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J Funct Anal, 2000, 173:361-400
[2] Otto F. The geometry of dissipative evolution equations:the porous medium equation. Commun Partial Differ Equ, 2001, 26(1/2):101-174
[3] Ambrosio L, Gigli N, Savaré G. Gradient Flows in Metric Spaces and in the Space of Probability Measures. ETH Zürich. Basel:Birkhäuser Verlag, 2005
[4] Li S, Li X. W-entropy formulas and Langevin deformation of flows on the Wasserstein space over Riemannian manifolds. 2016. arXiv:1604.02596v1
[5] Li S, Li X. W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds. Sci China Math, 2018, 61:1385-1406
[6] Lott J. Some geometric calculation on Wasserstein space. Commun Math Phys, 2008, 277:423-437
[7] Bakry D, Emery M. Diffusion hypercontractivities. Sém de Probab XIX, 1985, 19:177-206
[8] Sturm K T. On the geometry of metric measure spaces. Acta Math, 2006, 196:65-131
[9] Sturm K T, Von Renesse M K. Transport inequalities, gradient estimates, entropy and Ricci curvature. Comm Pure Appl Math, 2005, 58(7):923-940
[10] Lott J, Villani C. Ricci curvature for metric-measure spaces via optimal transport. Ann of Math, 2009, 169(3):903-991
[11] Gigli N. On the inverse implication of Brenier-McCann theorems and the structure of (P2(M), W2). Methods Appl Anal, 2011, 18(2):127-158
[12] Albeverio S, Kondratiev Y G, Röckner M. Diffferential geometry of Poisson spaces. C R Acad Sci Paris Série I Math, 1996, 323:1129-1134
[13] Ren P, Wang F. Derivative formula in measure on Riemannian manifolds. Bull Lond Math Soc, 2021, doi:10.1112/blms.12542
[14] Buckdahn R, Li J, Peng S, etal. Mean-field stochastic differential equations and associated PDEs. Ann Prob, 2017, 45(2):824-878
[15] Wang F. Image-dependent conditional McKean-Vlasov SDEs for measure-valued diffusion processes. J Evol Equ, 2021, 21:2009-2045
[16] Villani C. Optimal Transport, Old and New. Berlin:Springer-Verlag, 2009
[17] Villani C. Topics in Optimal Transportation. Providence Ehode Island:Amer Math Soc, 2003
[18] Fang S, Shao J. Fokker-Planck equation with respect to heat measures on loop groups. Bull Sci Math, 2011, 135(6/7):775-794
[19] Kunita H. Stochastic Flows and Stochastic Differentail Equations. Cambridge University Press, 1990
[20] Cruzeiro A B. Equations différentielles sur l'espace de Wiener et formules de Cameron-Martin non linéaires. J Funct Anal, 1983, 54:206-227
[21] Malliavin P. Stochastic Analysis. Vol 313 of Grundlehren der Mathematischen Wissenschaften. Berlin:Springer-Verlag, 1997
[22] Li X. On the strong Lp-Hodge decomposition over complete Riemannian manifolds. J Funct Anal, 2009, 257:3617-3646
[23] Benamou J D, Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer Math, 2000, 84(3):375-393
[24] Brenier Y. Polar factorization and monotone rearrangement of vector valued functions. Comm. Pure Appl Math, 1991, 44(4):375-417
[25] McCann R J. Polar factorization of maps on Riemannian manifolds. Geo Funct Anal, 2001, 11(8):589-608
[26] Ambrosio L, Gigli N. Construction of the parallel transport in the Wasserstein space. Methods Appl Anal, 2008, 15(1):1-30 |