K. Ciosmak

activity

20162026

collaborators

10 papers

math.FA2026

Absolutely minimising Lipschitz extensions between Hilbert spaces

Krzysztof J. Ciosmak

Every Lipschitz map from a closed subset of a real Hilbert space into a real Hilbert space has an absolutely minimising Lipschitz extension: an extension whose Lipschitz constant o…

math.MG2026

Measure contraction property on isometric leaves and monotone fibres

Krzysztof J. Ciosmak

For finite measures with positive densities on convex Euclidean supports, we prove that $M C P (κ, N)$ passes with unchanged parameters to almost every isometric leaf of an arbitrary n…

math.CV2023

Cartan-Thullen theorem and Levi problem in context of generalised convexity

Krzysztof J. Ciosmak

We demonstrate that the Cartan-Thullen theorem and its generalisation to the context of generalised convexity, which we establish herein, can be regarded as consequences of the cla…

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.FA2020

Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions

Krzysztof J. Ciosmak

We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of p…

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…

math.FA2019

Continuity of extensions of Lipschitz maps

Krzysztof J. Ciosmak

We establish the sharp rate of continuity of extensions of $R^{m}$ -valued $1$ -Lipschitz maps from a subset $A$ of $R^{n}$ to a $1$ -Lipschitz maps on $R^{n}$ . W…

math.CV2016

Differentiable functions on modules and the equation $g r a d (w) = M g r a d (v)$

Krzysztof Ciosmak

Let $A$ be a finite-dimensional, commutative algebra over $R$ or $C$ . The notion of $A$ -differentiable functions on $A$ is extended to the notion of $A$ -different…

Absolutely minimising Lipschitz extensions between Hilbert spaces

Measure contraction property on isometric leaves and monotone fibres

Cartan-Thullen theorem and Levi problem in context of generalised convexity

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

Optimal transport of vector measures

Leaves decompositions in Euclidean spaces

Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions

Leaves decompositions in Euclidean spaces and optimal transport of vector measures

Continuity of extensions of Lipschitz maps

Differentiable functions on modules and the equation grad(w)=Mgrad(v)

Differentiable functions on modules and the equation $g r a d (w) = M g r a d (v)$