2023/11/06 by Ahn, Jonghyeon, Kerman, Ely · 1 citation
#53D05 52A20 52A40 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2311.02870
In this work we investigate subsets of ℝ2n with the property that their mean width can not be decreased by the action of natural classes of symplectomorphisms. A common theme of our results is that toric symmetry is a preferred feature of subsets that are in optimal symplectic position with respect to the mean width. Among other things, we prove that the mean width of a toric domain can not be decreased by any linear symplectic map. We also show that toric convex domains are critical points of the mean width under all symplectic deformations.