The 2/3 - convergence rate for the Poisson bracket

Details The 2/3 - convergence rate for the Poisson bracket The 2/3 - convergence rate for the Poisson bracket

2008-02-26

arxiv.org/abs/0802.3792v4

Mathematics

Symplectic Geometry

Scientific paper

In this paper we introduce a new method for approaching the C^0 - rigidity results for the Poisson bracket. Using this method, we provide a different proof for the lower semi-continuity under C^0 perturbations, for the uniform norm of the Poisson bracket. We find the precise rate for the modulus of the semi-continuity. This extends the previous results of Cardin-Viterbo, Zapolsky, Entov and Polterovich. Using our method, we prove a C^0 - rigidity result in the spirit of the work of Humiliere. We also discuss a general question of the C^0 - rigidity for multilinear differential operators.

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