K. Ciosmak

collaborators

4 papers

math.FA2021

Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures

Krzysztof J. Ciosmak

We characterise equality cases in matrix Hölder's inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the represe…

math.FA2021

Optimal transport of vector measures

Krzysztof J. Ciosmak

We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with tota…

math.MG2021

Leaves decompositions in Euclidean spaces

Krzysztof J. Ciosmak

We partly extend the localisation technique from convex geometry to the multiple constraints setting. For a given $1$ -Lipschitz map $u : R^{n} \to R^{m}$ , $m \leq n$ ,…

math.MG2019

Leaves decompositions in Euclidean spaces and optimal transport of vector measures

Krzysztof J. Ciosmak

For a given $1$ -Lipschitz map $u : R^{n} \to R^{m}$ we define a partition, up to a set of Lebesgue measure zero, of $R^{n}$ into maximal closed convex sets su…