2006/03/16 by Shiri Artstein-Avidan, Artstein-Avidan, Shiri, Yaron Ostrover +1 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.math/0603411
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.