Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications

Abstract

In this paper we construct analogues of Ekeland-Hofer and 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 $c_{\mathrm{EH}}$ and $c_{\mathrm{HZ}}$, and a theorem by Evgeni Neduv).

Latex, 59 pages. Final version. To appear in The Journal of Geometric Analysis. The preprint arXiv:1903.01116v2[math.SG] was split into two papers. This is one of them. Another is arXiv:2302.12102

References in corpus (1)

• On the Almost Everywhere Continuity

Cited by in corpus (4)

• Coisotropic Ekeland-Hofer capacities
• Representation formula for symmetric symplectic capacity and applications
• Coisotropic Hofer-Zehnder capacities of convex domains and related results
• Higher $P$-symmetric Ekeland-Hofer capacities