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On Symplectic Capacities and Volume Radius

Shiri Artstein-Avidan·Yaron Ostrover
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Abstract

In this work we discuss a conjecture of Viterbo relating the symplectic capacity of a convex body and its volume. The conjecture states that among all 2n-dimensional convex bodies with a given volume the euclidean ball has maximal symplectic capacity. We present a proof of this fact up to a logarithmic factor in the dimension, and many classes of bodies for which this holds up to a universal constant.

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Shiri Artstein-Avidan, Yaron Ostrover. 2006-04-19. On Symplectic Capacities and Volume Radius. https://arxiv.org/abs/math/0603411

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