Positive loops and L∞-contact systolic inequalities

• Verfasst von: Albers, Peter [VerfasserIn]
• Verfasst von: Fuchs, Urs [VerfasserIn]
• Verfasst von: Merry, Will J. [VerfasserIn]
• Titel: Positive loops and L∞-contact systolic inequalities
• Verf.angabe: Peter Albers, Urs Fuchs, Will J. Merry
• Umfang: 31 S.
• Fussnoten: Das Zeichen ∞ erscheint stets hochgestellt ; Gesehen am 15.03.2018
• Titel Quelle: Enthalten in: Selecta mathematica
• Jahr Quelle: 2017
• Band/Heft Quelle: 23(2017), 4, S. 2491-2521
• ISSN Quelle: 1420-9020
• DOI: doi:10.1007/s00029-017-0338-2
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1571085106

Abstract

We prove an inequality between the L∞-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 et al. (J Symplectic Geom 14:1013-1031, 2016). As corollaries of the inequality we deduce various results. E.g. we prove that certain periodic Reeb flows are the unique minimisers of the L∞-norm. Moreover, we establish L∞-type contact systolic inequalities in the presence of a positive loop.