Symplectic variations of convex bodies and the mean width
arXiv:2311.02870
Abstract
In this work, we study convex bodies in $\RR^{2n}$ with the property that their mean width cannot be infinitesimally decreased by symplectomorphisms. The common theme of our results is that toric symmetry is a preferred feature of convex bodies with this property.
25 pages, 2 figures