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arXiv · 1008.0661

On the Uniqueness of Hofer's Geometry

Lev Buhovsky·Yaron Ostrover
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Abstract

We study the class of norms on the space of smooth functions on a closed symplectic manifold, which are invariant under the action of the group of Hamiltonian diffeomorphisms. Our main result shows that any such norm that is continuous with respect to the $C^{\infty}$-topology, is dominated from above by the $L_{\infty}$-norm. As a corollary, we obtain that any bi-invariant Finsler pseudo-metric on the group of Hamiltonian diffeomorphisms that is generated by an invariant norm that satisfies the aforementioned continuity assumption, is either identically zero or equivalent to Hofer's metric.

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Lev Buhovsky, Yaron Ostrover. 2010-08-03. On the Uniqueness of Hofer's Geometry. https://arxiv.org/abs/1008.0661

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