Higher index capacities do not satisfy the symplectic Brunn-Minkowski inequality
arXiv:2010.13603
Abstract
In this paper we prove that the symplectic Brunn-Minkowski inequality, established by Artstein-Avidan and Ostrover for the Ekeland-Hofer-Zehnder capacity, fails to hold for the Gutt-Hutchings capacities of index greater than one.
9 pages, 1 figure, to appear in the Israel Journal of Mathematics