We prove that the Floer complex associated with a convex Hamiltonian function on is isomorphic to the Morse complex of Clarke’s dual action functional 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.
"Symplectic homology of convex domains and Clarke’s duality." Duke Math. J. 171 (3) 739 - 830, 15 February 2022. https://doi.org/10.1215/00127094-2021-0025