45 citations · 194 across the 35 of their papers we have counts for
45 papers
Length spectrum rigidity and flexibility of spheres of revolution with one equator
Alberto Abbondandolo, Marco Mazzucchelli
We define a notion of marked length spectrum for -symmetric Riemannian metrics on the two-sphere having only one equator. We prove that isospectral metrics in this class have…
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…
Infinite-volume states with irreducible localization sets for gradient models on trees
Alberto Abbondandolo, Florian Henning, Christof Kuelske +1
We consider general classes of gradient models on regular trees with values in a countable Abelian group such as or , in regimes of strong coupling (…
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…