Positive loops and $L^{\infty}$-contact systolic inequalities
Symplectic Geometry
2017-09-26 v3 Differential Geometry
Abstract
We prove an inequality between the -norm of the contact Hamiltonian of a positive loop of contactomorphims and the minimal Reeb period. This implies that there are no small positive loops on hypertight or Liouville fillable contact manifolds. Non-existence of small positive loops for overtwisted 3-manifolds was proved by Casals-Presas-Sandon in [CPS16]. As corollaries of the inequality we deduce various results. E.g. we prove that certain periodic Reeb flows are the unique minimizers of the -norm. Moreover, we establish -type contact systolic inequalities in the presence of a positive loop.
Keywords
Cite
@article{arxiv.1602.01383,
title = {Positive loops and $L^{\infty}$-contact systolic inequalities},
author = {Peter Albers and Urs Fuchs and Will J. Merry},
journal= {arXiv preprint arXiv:1602.01383},
year = {2017}
}
Comments
26 pages, 6 figures; v2: corrected an error, changed statements of main theorems; v3: accepted version, to appear in Selecta Mathematica