Publications on optimal transport, gradient flows and geodesics
1. A new optimal transport distance on the space of finite Radon measures, with S. Kondratyev and L. Monsaingeon, Adv. Differential Equations 21 (2016) 1117-1164.
2. A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow, J. Differential Equ. 261 (2016) 2784–2808 (with S. Kondratyev and L. Monsaingeon).
3. A new multicomponent Poincaré-Beckner inequality (with S. Kondratyev and L. Monsaingeon), J. Funct. Anal. 272 (2017) 3281-3310.
4. Generalized solutions for inextensible string equations, with Y. Şengül, J. Diff. Equ., 262(6):3610–3641, 2017.
5. The gradient flow of the potential energy on the space of arcs, with W. Shi, to appear in CVPDE.
6. Uniformly compressing mean curvature flow, with W. Shi, to appear in J. Geom. Anal.
7. Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy, with S. Kondratyev, submitted.
8. Spherical Hellinger-Kantorovich gradient flows, with S. Kondratyev, to appear in SIAM J. Math. Anal.
9. Convex Sobolev inequalities related to unbalanced optimal transport, with S. Kondratyev, preprint.
10. On optimal transport of matrix-valued measures, with Y. Brenier, preprint.