Positive loops and L∞-contact systolic inequalities
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28 June 2017
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| In: |
Selecta mathematica
Year: 2017, Volume: 23, Issue: 4, Pages: 2491-2521 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-017-0338-2 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00029-017-0338-2 Verlag, Volltext: https://link.springer.com/article/10.1007/s00029-017-0338-2 
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| Author Notes: | Peter Albers, Urs Fuchs, Will J. Merry |
| Summary: | 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. |
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| Item Description: | Das Zeichen ∞ erscheint stets hochgestellt Gesehen am 15.03.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-017-0338-2 |