Positive loops and L -contact systolic inequalities

Peter Albers, Urs Fuchs, Will J. Merry

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5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2491-2521
Number of pages31
JournalSelecta Mathematica
Issue number4
Publication statusPublished - 1 Oct 2017
Externally publishedYes


  • 53D10
  • 57R58

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