JournalscmhVol. 90, No. 1pp. 1–21

New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians

  • Vincent Humilière

    Université Pierre et Marie Curie, Paris, France
  • Rémi Leclercq

    Université Paris-Sud, Orsay, France
  • Sobhan Seyfaddini

    University of California, Berkeley, USA
New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians cover
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Abstract

We prove a new variant of the energy-capacity inequality for closed rational symplectic manifolds (as well as certain open manifolds such as R2n\mathbb R^{2n}, cotangent bundle of closed manifolds…) and we derive some consequences to C0C^0–symplectic topology. Namely, we prove that a continuous function which is a uniform limit of smooth normalized Hamiltonians whose flows converge to the identity for the spectral (or Hofer’s) distance must vanish. This gives a new proof of uniqueness of continuous generating Hamiltonian for hameomorphisms. This also allows us to improve a result by Cardin and Viterbo on the C0C^0–rigidity of the Poisson bracket.

Cite this article

Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini, New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians. Comment. Math. Helv. 90 (2015), no. 1, pp. 1–21

DOI 10.4171/CMH/343