English

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.

Keywords

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

R2 v1 2026-06-22T02:46:09.783Z