2 citations · 4 across the 22 of their papers we have counts for
12 papers · 1 filter
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…
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…
Stability and the equality case in the B-theorem
Orli Herscovici, Galyna V. Livshyts, Liran Rotem +1
In this paper, we show the stability, and characterize the equality cases in the strong B-inequality of Cordero-Erasquin, Fradelizi and Maurey \cite{B-conj}. As an application, we…
New bounds on the minimal dispersion
Alexander E. Litvak, Galyna V. Livshyts
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in . This improves upper bounds for the minimal dispersion of a point s…
A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures
Galyna V. Livshyts
We show that for any log-concave measure on , any pair of symmetric convex sets and , and any $$μ((1-λ) K+λL)^{c_n}\geq (1-λ) μ(K)^{c_n}+λμ(L…
On a conjectural symmetric version of Ehrhard's inequality
Galyna V. Livshyts
We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex symmetric sets with respect to the Gaussian measure. Namely, letting $J_{k-1}(s)=\int^s_0 t^{…
On the local version of the Log-Brunn-Minkowski conjecture and some new related geometric inequalities
Alexander V. Kolesnikov, Galyna V. Livshyts
We prove that for any semi-norm on and any symmetric convex body in \begin{equation}\label{ineq-abs2} \int_{\partial K} \frac{\|n_x\…
Some remarks about the maximal perimeter of convex sets with respect to probability measures
Galyna V. Livshyts
In this note we study the maximal perimeter of a convex set in with respect to various classes of measures. Firstly, we show that for a probability measure on $…
The lower bound for Koldobsky's slicing inequality via random rounding
Bo'az Klartag, Galyna V. Livshyts
We study the lower bound for Koldobsky's slicing inequality. We show that there exists a measure and a symmetric convex body , such that for all $ξ\in…
Cube is a strict local maximizer for the illumination number
Galyna Livshyts, Konstantin Tikhomirov
It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in can be illuminated by at most light sources, and, moreover, $…
Randomized coverings of a convex body with its homothetic copies, and illumination
Galyna Livshyts, Konstantin Tikhomirov
We present a probabilistic model of illuminating a convex body by independently distributed light sources. In addition to recovering C.A. Rogers' upper bounds for the illumination…
On the stability of Brunn-Minkowski type inequalities
Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti
Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang \cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequali…