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arxiv: 1304.7037 · v2 · pith:O4ITZJCSnew · submitted 2013-04-25 · 🧮 math.GT · math.DG· math.SG

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

Michael Brandenbursky , Egor Shelukhin This is my paper
classification 🧮 math.GT math.DGmath.SG
keywords groupp-metrictwo-spherealongarea-preservingbi-lipschitzdiffeomorphismsdimension
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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.

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  1. Quasimorphisms on surfaces and continuity in the Hofer norm

    math.SG 2019-06 unverdicted novelty 6.0

    Many known quasimorphisms on surfaces fail to be continuous or Lipschitz in the Hofer norm, except for the Calabi quasimorphism on the sphere and induced versions on genus-zero surfaces.