2 citations · 4 across the 9 of their papers we have counts for
9 papers · 1 filter
The Complex Illumination Problem
Liran Rotem, Alon Schejter, Boaz A. Slomka
We formulate a complex analog of the celebrated Levi-Hadwiger-Boltyanski illumination (or covering) conjecture for complex convex bodies in C^n, as well as its (non-comparable) fra…
Vertex generated polytopes
Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka
In this paper we define and investigate a class of polytopes which we call "vertex generated" consisting of polytopes which are the average of their and dimensional faces.…
Boundary restricted Brunn-Minkowski inequalities
Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka
In this paper we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V.~Milman regarding the volume of $\part…
A Remark on discrete Brunn-Minkowski type inequalities via transportation of measure
Boaz A. Slomka
We give an alternative proof for discrete Brunn-Minkowski type inequalities, recently obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger weight…
Discrete variants of Brunn-Minkowski type inequalities
Diana Halikias, Bo'az Klartag, Boaz A. Slomka
We present an alternative, short proof of a recent discrete version of the Brunn-Minkowski inequality due to Lehec and the second named author. Our proof also yields the four funct…
Improved bounds for Hadwiger's covering problem via thin-shell estimates
Han Huang, Boaz A. Slomka, Tomasz Tkocz +1
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number is such that every convex body in ${\mathbb R}…
Ulam Floating Body
Han Huang, Boaz A. Slomka, Elisabeth M. Werner
We study a new construction of bodies from a given convex body in which are isomorphic to (weighted) floating bodies. We establish several properties of this new c…
Approximations of convex bodies by measure-generated sets
Han Huang, Boaz A. Slomka
Given a Borel measure on , we define a convex set by \[ M(μ)=\bigcup_{\substack{0\le f\le1,\\ \int_{{\mathbb R}^{n}}f\,{\rm d}μ=1 } }\left\{ \int_{{\mathbb R}^…
On weighted covering numbers and the Levi-Hadwiger conjecture
Shiri Artstein-Avidan, Boaz A. Slomka
We define new natural variants of the notions of weighted covering and separation numbers and discuss them in detail. We prove a strong duality relation between weighted covering a…