Coisotropic Hofer-Zehnder capacities of convex domains and related results

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.

Automated summary

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