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arXiv · 1209.2134

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

Vincent Humilière·Rémi Leclercq·Sobhan Seyfaddini
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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 cotangent bundle of closed manifolds...) and we derive some consequences to C^0-symplectic topology. Namely, we prove that a continuous function which is a uniform limit of smooth 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 C^0-rigidity of the Poisson bracket.

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Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini. 2012-09-10. New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians. https://doi.org/10.4171/cmh/343

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