The 2/3 - convergence rate for the Poisson bracket
Buhovsky, Lev
Original · EN
In this paper we introduce a new method for approaching the C⁰ - rigidity results for the Poisson bracket. Using this method, we provide a different proof for the lower semi-continuity under C⁰ 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 C⁰ - rigidity result in the spirit of the work of Humiliere. We also discuss a general question of the C⁰ - rigidity for multilinear differential operators.
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