9 papers
A logarithmic Brascamp--Lieb variance inequality
Alexander V. Kolesnikov
We prove a strengthened Brascamp--Lieb inequality for even log-concave measures whose positive sublevel bodies satisfy the local logarithmic Brunn--Minkowski inequality. The conclu…
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…