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math.MG2026
Contractibility of space of symplectically self-polar convex bodies
Mark Berezovik
Symplectically self-polar bodies have been introduced recently. They appeared in the context of Mahler's conjecture and in the context of symplectic outer billiard dynamics. In thi…
math.MG2025★ 1 cited
Symplectic polarity and Mahler's conjecture
Mark Berezovik, Roman Karasev
We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and i…
math.MG2025
Symplectically self-polar polytopes of minimal capacity
Mark Berezovik
In this paper we continue the study of symplectically self-polar convex bodies started in arXiv:2211.14630. We construct symplectically self-polar convex bodies of the minimal Ekel…