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Equivalent definition of the Kantorovich-Fisher-Rao distance

Well, when we wrote the paper we were not really concerned with full rigor at this stage, all we wanted to emphasize was that the "KFR" distance (by now rather the WFR or HK distance, as in ...
2 votes

Strict convexity of the cost function is enough to ensure the existence and uniqueness of the optimal transport map

First a comment: you write (before stating your Theorem 3.14) that "The existence and uniqueness of the solution of the Monge Problem is guaranteed if $c$ is strictly convex and the supports of $\...
4 votes

Gradient descent relaxation dynamics of a Euler-Lagrange equation

The usual way to ensure the convergence of the steepest descent formulation of the Euler-Lagrange equations, is to introduce a friction term, see The Calculus of Variations by Jeff Calder. Instead of $...

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