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2001 Hofer–Zehnder capacity and length minimizing Hamiltonian paths
Dusa McDuff, Jennifer Slimowitz
Geom. Topol. 5(2): 799-830 (2001). DOI: 10.2140/gt.2001.5.799


We use the criteria of Lalonde and McDuff to show that a path that is generated by a generic autonomous Hamiltonian is length minimizing with respect to the Hofer norm among all homotopic paths provided that it induces no non-constant closed trajectories in M. This generalizes a result of Hofer for symplectomorphisms of Euclidean space. The proof for general M uses Liu–Tian’s construction of S1–invariant virtual moduli cycles. As a corollary, we find that any semifree action of S1 on M gives rise to a nontrivial element in the fundamental group of the symplectomorphism group of M. We also establish a version of the area-capacity inequality for quasicylinders.


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Dusa McDuff. Jennifer Slimowitz. "Hofer–Zehnder capacity and length minimizing Hamiltonian paths." Geom. Topol. 5 (2) 799 - 830, 2001.


Received: 12 January 2001; Revised: 9 October 2001; Accepted: 9 November 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1002.57056
MathSciNet: MR1871405
Digital Object Identifier: 10.2140/gt.2001.5.799

Primary: 57R17
Secondary: 53D05 , 57R57

Keywords: hamiltonian diffeomorphisms , Hofer norm , Hofer–Zehnder capacity , symplectic geometry

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2001
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