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

Michael Brandenbursky; Egor Shelukhin

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arXiv · 1304.7037

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

Michael Brandenbursky·Egor Shelukhin

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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.

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BibTeX RIS

Michael Brandenbursky, Egor Shelukhin. 2014-06-15. On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere. https://arxiv.org/abs/1304.7037

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