4 papers
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…
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}^…
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…