Publications related to optimal transport, gradient flows and metric geometry

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, Calc. Var. 58 (2019), art. 59.

6. Uniformly compressing mean curvature flow, with W. Shi, J. Geom. Anal. 29 (2019) 3055–3097.

7. Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy, with S. Kondratyev, J. Funct. Anal. 278 (2020) 108310.

8. Spherical Hellinger-Kantorovich gradient flows, with S. Kondratyev, SIAM J. Math. Anal 51 (2019) 2053–2084. Corrigendum

9. Convex Sobolev inequalities related to unbalanced optimal transport, with S. Kondratyev, J. Diff. Equ. 268 (2020) 3705-3724.

10. On optimal transport of matrix-valued measures, with Y. Brenier, SIAM J. Math. Anal. 52 (2020) 2849-2873.

11. The Schrödinger problem on the non-commutative Fisher-Rao space, with. L. Monsaingeon, Calc. Var. Partial Differential Equations 60 (2021), art. 14. 

12. Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems, Arch. Rational Mech. Anal. 243 (2022) 1653-1698.

13. Overdamped Dynamics of a Falling Inextensible Network: Existence of Solutions, with A. Telciyan, Interfaces Free Bound., to appear.

14. The dynamical Schrödinger problem in abstract metric spaces, with L. Monsaingeon and L. Tamanini, Adv. Math., to appear.

15. Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps, with H. Lavenant, L. Monsaingeon and L. Tamanini, Calc. Var. Partial Differential Equations, to appear.

16. Schrödinger Encounters Fisher and Rao: A Survey (with. L Monsaingeon). In: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science, vol. 12829. Springer, Cham.