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arXiv · 1609.08891

Rigidity of the L^p norm of the Poisson bracket on surfaces

Karina Samvelyan·Frol Zapolsky
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Abstract

For a symplectic manifold $M$ let $\{\cdot,\cdot\}$ be the corresponding Poisson bracket. In this note we prove that the functional $(F,G) \mapsto \|\{F,G\}\|_{L^p(M)}$ is lower-semicontinuous with respect to the $C^0$-norm on $C^\infty_c(M)$ when $\dim M = 2$ and $p < \infty$, extending previous rigidity results for $p = \infty$ in arbitrary dimension.

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Karina Samvelyan, Frol Zapolsky. 2016-09-28. Rigidity of the L^p norm of the Poisson bracket on surfaces. https://arxiv.org/abs/1609.08891

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