English

Higher index capacities do not satisfy the symplectic Brunn-Minkowski inequality

Symplectic Geometry 2020-10-27 v1

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.

Keywords

Cite

@article{arxiv.2010.13603,
  title  = {Higher index capacities do not satisfy the symplectic Brunn-Minkowski inequality},
  author = {Ely Kerman and Yuanpu Liang},
  journal= {arXiv preprint arXiv:2010.13603},
  year   = {2020}
}

Comments

9 pages, 1 figure, to appear in the Israel Journal of Mathematics