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

Karina Samvelyan, Frol Zapolsky

Research output: Contribution to journalArticlepeer-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 Cc (M) when dim M = 2 and p < ∞, extending previous rigidity results for p = ∞ in arbitrary dimension.

Original languageEnglish
Pages (from-to)28-37
Number of pages10
JournalElectronic Research Announcements in Mathematical Sciences
Volume24
DOIs
StatePublished - 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

  • Mathematics (all)

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