45 citations · 194 across the 35 of their papers we have counts for
22 papers · 1 filter
On closed characteristics of minimal action on a convex three-sphere
Alberto Abbondandolo, Oliver Edtmair, Jungsoo Kang
We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in bounds a disk-like global surface of section. A corollary is that…
Symplectic capacities of domains close to the ball and Banach-Mazur geodesics in the space of contact forms
Alberto Abbondandolo, Gabriele Benedetti, Oliver Edtmair
We prove that all normalized symplectic capacities coincide on smooth domains in which are -close to the Euclidean ball, whereas this fails for some smooth domai…
Lorentz-Finsler metrics on symplectic and contact transformation groups
Alberto Abbondandolo, Gabriele Benedetti, Leonid Polterovich
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric quest…
Higher systolic inequalities for 3-dimensional contact manifolds
Alberto Abbondandolo, Christian Lange, Marco Mazzucchelli
A contact form is called Besse when the associated Reeb flow is periodic. We prove that Besse contact forms on closed connected 3-manifolds are the local maximizers of suitable hig…
On the local systolic optimality of Zoll contact forms
Alberto Abbondandolo, Gabriele Benedetti
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of th…
Symplectic homology of convex domains and Clarke's duality
Alberto Abbondandolo, Jungsoo Kang
We prove that the Floer complex that is associated with a convex Hamiltonian function on is isomorphic to the Morse complex of Clarke's dual action functional tha…