G. Livshyts

activity

20132026

most citedMaximal Surface Area of a convex set in

R^{n}

with respect to log concave rotation invariant measures

2 citations · 4 across the 22 of their papers we have counts for

collaborators

Showing 2017Show all

2 papers · 1 filter

math.MG2017

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 $R^{n}$ can be illuminated by at most $2^{n}$ light sources, and, moreover, $…

math.DG2017

A note on the quantitative local version of the log-Brunn-Minkowski inequality

Andrea Colesanti, Galyna V. Livshyts

We prove that the log-Brunn-Minkowski inequality \begin{equation*} |λK+_0 (1-λ)L|\geq |K|^λ|L|^{1-λ} \end{equation*} (where $∣ \cdot ∣$ is the Lebesgue measure and $+_{0}$ is the so-ca…