On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky; Egor Shelukhin

doi:10.4310/MRL.2015.v22.n5.a1

On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky, Egor Shelukhin

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

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 language	American English
Pages (from-to)	1275-1294
Number of pages	20
Journal	Mathematical Research Letters
Volume	22
Issue number	5
DOIs	https://doi.org/10.4310/MRL.2015.v22.n5.a1
State	Published - 1 Jan 2015

Keywords

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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.4310/MRL.2015.v22.n5.a1

Cite this

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