On Symplectic Capacities and Volume Radius

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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.
22 pages

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Symplectic Geometry, 53D05, 53C15, 46B07, 52A20, 46B20

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http://salesiana.dossiersoluciones.com/handle/123456789/110233

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603411
 http://arxiv.org/abs/math/0603411

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arXiv