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arXiv · 2310.14998

Symplectically self-polar polytopes of minimal capacity

Mark Berezovik
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Abstract

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 Ekeland-Hofer-Zehnder capacity. This in turn proves that the lower bound for the Ekeland-Hofer-Zehnder capacity for centrally symmetric convex bodies obtained in arXiv:1801.00242 cannot be improved. We also make some numerical experiments and speculations regarding the minimal volume of symplectically self-polar convex bodies.

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Mark Berezovik. 2023-10-23. Symplectically self-polar polytopes of minimal capacity. https://doi.org/10.1007/s40316-025-00251-0

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