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<p>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 its Euclidean polar. We also establish lower and upper bounds for symplectic capacities of symplectically self-polar bodies.</p>

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Symplectic polarity and Mahler’s conjecture

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Mark Berezovik,
  • Roman Karasev

摘要

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 its Euclidean polar. We also establish lower and upper bounds for symplectic capacities of symplectically self-polar bodies.