2 citations · 4 across the 9 of their papers we have counts for
14 papers
The Scaled Polarity transform and related inequalities
Shoni Gilboa, Alexander Segal, Boaz A. Slomka
In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform can be rescaled so that the Mahl…
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…
Isobarycentric Inequalities
Shoni Gilboa, Pazit Haim-Kislev, Boaz Slomka
We prove the following isoperimetric type inequality: Given a finite absolutely continuous Borel measure on , halfspaces have maximal measure among all subsets with…
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}^…
Functional Covering Numbers
Shiri Artstein-Avidan, Boaz A. Slomka
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and cove…
The Fundamental Theorems of Affine and Projective Geometry Revisited
Shiri Artstein-Avidan, Boaz A. Slomka
The fundamental theorem of affine geometry is a classical and useful result. For finite-dimensional real vector spaces, the theorem roughly states that a bijective self-mapping whi…
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…
A note on Santaló inequality for the polarity transform and its reverse
Shiri Artstein-Avidan, Boaz Slomka
We prove a Santaló and a reverse Santaló inequality for the polarity transform, which was recently re-discovered by Artstein-Avidan and Milman, in the class consisting of (even) lo…