Lagrangian non-squeezing and a geometric inequality

We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest nontrivial closed geodesic is at most half the area of the unit disc.Comment: minor changes, to appear in Math.

The annulus property of simple holomorphic discs

We show that any simple holomorphic disc admits the annulus property, i.e., each interior point is surrounded by an arbitrary small annulus consisting entirely of injective points. As an application we show that interior singularities of holomorphic discs can be resolved after slight perturbation of the almost complex structure. Moreover, for boundary points the analogue notion, the half-annulus property, is introduced and studied in detail.Comment: 23 pages, no figures, article rewritten, to appear in J. Symplectic Geo

Linking and closed orbits

We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology.Comment: We weakened the assumption to be of bounded geometr