Lagrangian Hofer-Zehnder Capacities and Energy-Capacity Inequalities

Rieser and I introduced a variation on the Hofer-Zehnder capacity, relative to a coisotropic submanifold. Revisiting this construction in the case in which the coisotropic submanifold is Lagrangian, we use a persistent homology approach to filtered Floer theory (following Polterovich and Shelukhin) to obtain two energy-capacity inequalities, a local one and a global one. We also show that one of these breaks down if we don't impose topological conditions on the admissible Hamiltonians. This suggests that our capacity is closely related to Barraud-Cornea's real Gromov radius. This is joint work with Antonio Rieser.