Reeb dynamics detects odd balls
Symplectic Geometry
2019-03-11 v2 Dynamical Systems
Geometric Topology
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.
Cite
@article{arxiv.1401.3598,
title = {Reeb dynamics detects odd balls},
author = {Hansjörg Geiges and Kai Zehmisch},
journal= {arXiv preprint arXiv:1401.3598},
year = {2019}
}
Comments
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