33 citations · 215 across the 34 of their papers we have counts for
5 papers · 1 filter
Boundary and lens rigidity for non-convex manifolds
Colin Guillarmou, Marco Mazzucchelli, Leo Tzou
We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected…
A characterization of Zoll Riemannian metrics on the 2-sphere
Marco Mazzucchelli, Stefan Suhr
The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2-sphere whose…
Closed geodesics with local homology in maximal degree on non-compact manifolds
Luca Asselle, Marco Mazzucchelli
We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with…
Minimal boundaries in Tonelli Lagrangian systems
Luca Asselle, Gabriele Benedetti, Marco Mazzucchelli
We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface . More specifically, we show that for every…
Infinitely many periodic orbits just above the Mañé critical value on the 2-sphere
Gabriele Benedetti, Marco Mazzucchelli
We introduce a new critical value for Tonelli Lagrangians on the tangent bundle of the 2-sphere without minimizing measures supported on a point. We show that $c_…