New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians
| Autor: | Humilière, Vincent, Leclercq, Rémi, Seyfaddini, Sobhan |
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| Rok vydání: | 2012 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.4171/CMH/343 |
| Popis: | 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. Comment: 18 pages. v2. Several minor changes. Reference list updated. To appear in Commentarii Mathematici Helvetici |
| Databáze: | arXiv |
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