G. Livshyts

activity

20242026

collaborators

7 papers

math.MG2026

A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures

Galyna V. Livshyts

We show that for any log-concave measure $I^¼$ on $R^{n}$ , any pair of symmetric convex sets $K$ and $L$ , and any $I^» \in [0, 1],$ $$Î¼((1-Î») K+Î»L)^{c_n}\geq (1-Î») Î¼(K)^{c_…

math.FA2026

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 $α$ -homogeneous potential $V$ is equivalent to a $p$ -Brunn--Minkowski inequali…

math.MG2025

On the polar of Schneider's difference body

JuliÃ¡n Haddad, Dylan Langharst, Galyna V. Livshyts +1

In 1970, Schneider introduced the $m$ th-order extension of the difference body $D K$ of a convex body $K \subset R^{n}$ , the convex body $D^{m} (K)$ in $R^{nm}$ . He conject…

math.PR2025

On the Smallest Singular Value of Log-Concave Random Matrices

Manuel Fernandez, Galyna V. Livshyts, Stephanie Mui

Let $A$ be an $N \times n$ random matrix whose entries are coordinates of an isotropic log-concave random vector in $R^{N n}$ . We prove sharp lower tail estimates for the sm…

math.FA2024

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…

math.AP2024

The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction

Andrea Colesanti, Elisa Francini, Galyna Livshyts +1

We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator $L (u) = I^ u - ⟨ \nabla u, x ⟩,$ as a function of the domain, is convex with…