21 citations · 122 across the 24 of their papers we have counts for
5 papers · 1 filter
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…
Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities
Luca Asselle, Gabriele Benedetti
In this paper we study some aspects of integrable magnetic systems on the two-torus. On the one hand, we construct the first non-trivial examples with the property that all magneti…
On a systolic inequality for closed magnetic geodesics on surfaces
Gabriele Benedetti, Jungsoo Kang
We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic…
On a local systolic inequality for odd-symplectic forms
Gabriele Benedetti, Jungsoo Kang
The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let b…
A local contact systolic inequality in dimension three
Gabriele Benedetti, Jungsoo Kang
Let be a contact form on a connected closed three-manifold . The systolic ratio of is defined as , where $T…