Rigidity of the Lp-norm of the poisson bracket on surfaces

Karina Samvelyan; Frol Zapolsky

doi:10.3934/era.2017.24.004

Rigidity of the L^p-norm of the poisson bracket on surfaces

Karina Samvelyan, Frol Zapolsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a symplectic manifold (M; w), let {,} be the correspond- ing Poisson bracket. In this note we prove that the functional (F;G) → ||{F;G}||Lp(M) is lower-semicontinuous with respect to the C⁰-norm on C^∞_c (M) when dim M = 2 and p < ∞, extending previous rigidity results for p = ∞ in arbitrary dimension.

Original language	English
Pages (from-to)	28-37
Number of pages	10
Journal	Electronic Research Announcements in Mathematical Sciences
Volume	24
DOIs	https://doi.org/10.3934/era.2017.24.004
State	Published - 13 May 2017

Bibliographical note

Publisher Copyright:
© 2016 American Institute of Mathematical Sciences.

Keywords

Lp-norm
Poisson bracket
Rigidity
Surfaces
Symplectic topology

ASJC Scopus subject areas

General Mathematics

Access to Document

10.3934/era.2017.24.004

Cite this

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abstract = "For a symplectic manifold (M; w), let \{,\} be the correspond- ing Poisson bracket. In this note we prove that the functional (F;G) → ||\{F;G\}||Lp(M) is lower-semicontinuous with respect to the C0-norm on C∞c (M) when dim M = 2 and p < ∞, extending previous rigidity results for p = ∞ in arbitrary dimension.",

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