On Symplectic Capacities and Volume Radius
辛几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0603411,
title = {On Symplectic Capacities and Volume Radius},
author = {Shiri Artstein-Avidan and Yaron Ostrover},
journal= {arXiv preprint arXiv:math/0603411},
year = {2007}
}
备注
22 pages