Combinatorial formulas for some generalized Ekeland-Hofer-Zehnder capacities of convex polytopes

Motivated by Pazit Haim-Kislev's combinatorial formula for the Ekeland-Hofer-Zehnder capacities of convex polytopes, we give corresponding formulas for psi-Ekeland-Hofer-Zehnder and coisotropic Ekeland-Hofer-Zehnder capacities of convex polytopes introduced by the second named author and others recently. Contrary to Pazit Haim-Kislev's subadditivity result for the Ekeland-Hofer-Zehnder capacities of convex domains, we show that the coisotropic Hofer-Zehnder capacities satisfy the superadditivity for suitable hyperplane cuts of two-dimensional convex domains.

Automated summary

Inspired by Pazit Haim-Kislev's work on Ekeland-Hofer-Zehnder capacities, we have derived corresponding formulas for psi-Ekeland-Hofer-Zehnder and coisotropic Ekeland-Hofer-Zehnder capacities of convex polytopes. Additionally, we have shown that the coisotropic Hofer-Zehnder capacities exhibit superadditivity for specific hyperplane cuts in two-dimensional convex domains, contrary to previous results.