4 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…