On the Uniqueness of Hofer's Geometry

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We study the class of pseudo-norms on the space of smooth functions on a closed symplectic manifold, which are invariant under the action of the group of Hamiltonian diffeomorphisms. Our main result shows that any such pseudo-norm that is continuous with respect to the C-topology, is dominated from above by the L-norm. As a corollary, we obtain that any bi-invariant Finsler pseudo-metric on the group of Hamiltonian diffeomorphisms that is generated by an invariant pseudonorm that satisfies the aforementioned continuity assumption, is either identically zero or equivalent to Hofer's metric.

Original languageEnglish
Pages (from-to)1296-1330
Number of pages35
JournalGeometric and Functional Analysis
Issue number6
StatePublished - Dec 2011


  • 22E65
  • 53D05
  • 58B20
  • Hamiltonian diffeomorphisms
  • Hofer's metric
  • bi-invariant Finsler metrics

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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