English

Symplectically self-polar polytopes of minimal capacity

Metric Geometry 2025-12-02 v2 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.2310.14998,
  title  = {Symplectically self-polar polytopes of minimal capacity},
  author = {Mark Berezovik},
  journal= {arXiv preprint arXiv:2310.14998},
  year   = {2025}
}