Generalizations of Ekeland–Hofer and Hofer–Zehnder Symplectic Capacities and Applications

Abstract

In this paper we construct analogues of the Ekeland–Hofer and the Hofer–Zehnder symplectic capacities based on a class of Hamiltonian boundary value problems motivated by Clarke’s and Ekeland’s work, and study generalizations of some important results about the original two capacities (for example, the famous Weinstein conjecture, representation formula for $$c_{\textrm{EH}}$$ and $$c_{\textrm{HZ}}$$ , and a theorem by Evgeni Neduv).