Author

A. Kolesnikov

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Preprint Oct 2026

Blaschke--Santal\'o inequalities with respect to costs

We study functional Blaschke--Santal\'o inequalities in which the inner product is replaced by a cost. An inequality on each orthant, combined with Steiner symmetrization, gives a sufficient condition for a cost inequality to hold for even convex functions. We apply this principle to a multiplicative cost defined on al...

A. Kolesnikov, G. Livshyts, L. Rotem · 0 citations

Preprint Oct 2026

A logarithmic Brascamp--Lieb variance inequality

We prove a strengthened Brascamp--Lieb inequality for even log-concave measures whose positive sublevel bodies satisfy the local logarithmic Brunn--Minkowski inequality. The conclusion can be written either by adding a rank-one term to the Hessian of the potential or by adding an explicit nonnegative remainder to the v...

A. Kolesnikov · 0 citations