Higher index capacities do not satisfy the symplectic Brunn-Minkowski inequality
Ely Kerman, Yuanpu Liang
TL;DR
This paper demonstrates that the symplectic Brunn-Minkowski inequality, valid for certain capacities, does not hold for Gutt-Hutchings capacities with index greater than one, revealing limitations of the inequality.
Contribution
It shows the failure of the symplectic Brunn-Minkowski inequality for higher index Gutt-Hutchings capacities, extending understanding of symplectic capacity inequalities.
Findings
The inequality holds for Ekeland-Hofer-Zehnder capacity.
Fails for Gutt-Hutchings capacities with index > 1.
Highlights limitations of symplectic capacity inequalities.
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.
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Taxonomy
TopicsPoint processes and geometric inequalities · Stochastic processes and statistical mechanics · Random Matrices and Applications