Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities
Metric Geometry
2018-04-26 v3
Abstract
In this note we apply the billiard technique to deduce some results on Viterbo's conjectured inequality between volume of a convex body and its symplectic capacity. We show that the product of a permutohedron and a simplex (properly related to each other) delivers equality in Viterbo's conjecture. Using this result as well as previously known equality cases, we prove some special cases of Viterbo's conjecture and interpret them as isoperimetric-like inequalities for billiard trajectories.
Keywords
Cite
@article{arxiv.1512.01657,
title = {Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities},
author = {Alexey Balitskiy},
journal= {arXiv preprint arXiv:1512.01657},
year = {2018}
}
Comments
15 pages, 5 figures. To appear in International Mathematics Research Notices. Former title "Equality cases in Viterbo's conjecture related to permutohedra"