83 citations · 134 across the 29 of their papers we have counts for
5 papers · 1 filter
Analysis of polarity
Shiri Artstein-Avidan, Yanir A. Rubinstein
We develop a differential theory for the polarity transform parallel to that for the Legendre transform, which is applicable when the functions studied are "geometric convex", name…
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…
Remarks about Mixed Discriminants and Volumes
Shiri Artstein-Avidan, Dan Florentin, Yaron Ostrover
In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in n-dimensions. Moreover, we discus…
From Symplectic Measurements to the Mahler Conjecture
Shiri Artstein-Avidan, Roman Karasev, Yaron Ostrover
In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains, and Mahler'…
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…