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

abstract

  • 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.

publication date

  • April 25, 2013