The 2/3 - convergence rate for the Poisson bracket
Symplectic Geometry
2010-02-27 v4 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.0802.3792,
title = {The 2/3 - convergence rate for the Poisson bracket},
author = {Lev Buhovsky},
journal= {arXiv preprint arXiv:0802.3792},
year = {2010}
}