8 papers
Blaschke--Santaló inequalities with respect to costs
Alexander V. Kolesnikov, Galyna V. Livshyts, Liran Rotem
We study functional Blaschke--Santaló inequalities in which the inner product is replaced by a cost. An inequality on each orthant, combined with Steiner symmetrization, gives a su…
Duality for a Martingale Transport Problem with Moment Constraints
Alexander V. Kolesnikov, Aleksandra Novikova, Kirill Sokolov
We consider a weak martingale optimal transport problem related to the martingale analogue of the Benamou--Brenier formula. In contrast to the classical setting, the second margina…
Homogeneous maximizers of the Blaschke--Santalo-type functionals
Alexander V. Kolesnikov
We study Blaschke--Santal{ó}-type inequalities for sets (functions) and a special class of cost functions. In particular, we prove new results about the reduction of the…
On p-Brunn-Minkowski and Brascamp-Lieb inequalities
Alexander V. Kolesnikov, Galyna Livshyts, Liran Rotem
We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with -homogeneous potential is equivalent to a -Brunn--Minkowski inequali…
On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities
Andrea Colesanti, Alexander Kolesnikov, Galyna Livshyts +1
In this paper, we study new extensions of the functional Blaschke-Santaló inequalities, and explore applications of such new inequalities beyond the classical setting of the standa…
Auctions and mass transportation
Alexander V. Kolesnikov
In this survey paper we present classical and recent results relating the auction design and the optimal transportation theory. In particular, we discuss in details the seminal res…