Symplectic homology of convex domains and Clarke's duality

Abstract

We prove that the Floer complex that is associated with a convex Hamiltonian function on ${\mathbb{R}}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated with the Fenchel-dual Hamiltonian. This isomorphism preserves the action filtrations. As a corollary, we obtain that the symplectic capacity from the symplectic homology of a convex domain with smooth boundary coincides with the minimal action of closed characteristics on its boundary.

80 pages, v2: corrections in the proof of Lemma A.3, Appendix B added

References in corpus (1)

• Functors and Computations in Floer homology with Applications Part II

Cited by in corpus (3)

• On the structure of Besse convex contact spheres
• Remarks on symplectic capacities of $p$-products
• Computing Reeb dynamics on 4d convex polytopes