On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere

2013/04/25 by Michael Brandenbursky, Brandenbursky, Michael, Egor Shelukhin +1 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1304.7037

17 pages, 1 figure; a revised manuscript correcting a mistake in the original version, the main result holds for p>2

openalex publication_date 2013/04/25 · arxiv created 2014/06/15 · arxiv updated 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the vector space R^d of any finite dimension d with the standard metric embeds in a bi-Lipschitz way into the group of area-preserving diffeomorphisms G of the two-sphere endowed with the L^p-metric for p>2. Along the way we show that the L^p-metric on the group G is unbounded for p>2 by elementary methods.

Cited by

• Large scale geometry of metrisable groups
• The L^p-diameter of the group of area-preserving diffeomorphisms of S²

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