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Displacement interpolations from a Hamiltonian point of view
One of the most well-known results in the theory of optimal transportation is
the equivalence between the convexity of the entropy functional with respect to
the Riemannian Wasserstein metric and the Ricci curvature lower bound of the
underlying Riemannian manifold. There are also generalizations of this result
to the Finsler manifolds and manifolds with a Ricci flow background. In this
paper, we study displacement interpolations from the point of view of
Hamiltonian systems and give a unifying approach to the above mentioned
results.Comment: 46 pages (A discussion on the Finsler case and a new example are
added
On the Jordan-Kinderlehrer-Otto scheme
In this paper, we prove that the Jordan-Kinderlehrer-Otto scheme for a family
of linear parabolic equations on the flat torus converges uniformly in space.Comment: 15 page
A Remark on the Potentials of Optimal Transport Maps
Optimal maps, solutions to the optimal transportation problems, are
completely determined by the corresponding c-convex potential functions. In
this paper, we give simple sufficient conditions for a smooth function to be
c-convex when the cost is given by minimizing a Lagrangian action.Comment: 20 page
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