Coisotropic Hofer-Zehnder capacities of convex domains and related results

TL;DR

This paper investigates the coisotropic Hofer-Zehnder capacities of convex domains, providing new formulas, estimates, and relations with existing capacities, along with corollaries and inequalities that extend previous results in symplectic geometry.

Contribution

It introduces representation formulas for these capacities in convex domains with special coisotropic submanifolds, advancing understanding of their properties and connections.

Findings

Derived new representation formulas for capacities

Established estimates and relations with Hofer-Zehnder capacity

Extended Brunn-Minkowski type inequalities to this setting

Abstract

We prove representation formulas for the coisotropic Hofer-Zehnder capacities of bounded convex domains with special coisotropic submanifolds and the leaf relation (introduced by Lisi and Rieser recently), study their estimates and relations with the Hofer-Zehnder capacity,give some interesting corollaries, and also obtain corresponding versions of a Brunn-Minkowski type inequality by Artstein-Avidan and Ostrover and a theorem by Evgeni Neduv.