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math.FA2026
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…
math.FA2026
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…