On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky, Egor Shelukhin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.

Original languageEnglish
Pages (from-to)1275-1294
Number of pages20
JournalMathematical Research Letters
Issue number5
StatePublished - 1 Jan 2015


  • Braid groups
  • Groups of Hamiltonian diffeomorphisms
  • L-metrics
  • Mapping class groups
  • Quasi-morphisms

ASJC Scopus subject areas

  • General Mathematics


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