Reeb dynamics detects odd balls

Abstract

We give a dynamical characterisation of odd-dimensional balls within the class of all contact manifolds whose boundary is a standard even-dimensional sphere. The characterisation is in terms of the non-existence of short periodic Reeb orbits.

15 pages. The proof of the energy estimate in v1 (Lemma 4) is incomplete. In v2 we circumvent this by working with a model involving Lagrangian boundary conditions instead of totally real ones. Parts of the holomorphic analysis in v1 for the case of totally real boundary conditions may be of independent interest

References in corpus (2)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Trapped Reeb orbits do not imply periodic ones

Cited by in corpus (8)

• Gromov compactness for holomorphic discs with totally real boundary conditions
• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• The Weinstein conjecture for connected sums
• The diffeomorphism type of symplectic fillings
• Periodic orbits in virtually contact structures
• Symplectic dynamics of contact isotropic torus complements
• The Chekanov torus in $S^2\times S^2$ is not real
• Two constructions of virtually contact structures