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's …

We show that the fundamental objects of the Lp-Brunn–Minkowski theory, namely the Lp-
affine surface areas for a convex body, are closely related to information theory: they are …

We prove Mahler's conjecture concerning the volume product of centrally symmetric, convex
bodies in R n in the case where n= 3. More precisely, we show that, for every 3-dimensional …

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler
conjecture for symmetric convex bodies. Our contributions include, in particular, simple self …

Sharp reverse affine isoperimetric inequalities for asymmetric Wulff shapes and their polars
are established, along with the characterization of all extremals. These new inequalities …

Mahler's conjecture predicts a sharp lower bound on the volume of the polar of a convex
body in terms of its volume. We confirm the conjecture for convex bodies with many …

Shadow systems are used to establish new asymmetric Lp volume product and asymmetric
Lp volume ratio inequalities, along with their equality conditions. These inequalities have …

Our purpose here is to give an overview of known results and open questions concerning
the volume product 𝒫 (K)= minz∈ K vol (K) vol ((K− z)∗) of a convex body K in ℝn. We …

arXiv:1404.6954v1 [math.SG] 28 Apr 2014 Page 1 arXiv:1404.6954v1 [math.SG] 28 Apr 2014
When Symplectic Topology Meets Banach Space Geometry Yaron Ostrover Abstract. In this …

A Fourier analytic proof of the Blaschke-Santaló Inequality Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 11, November 2015, Pages …