@article{1e58b8ab9ac74c1ea70e034cba99065f,
title = "On the Uniqueness of Hofer's Geometry",
abstract = "We study the class of pseudo-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 pseudo-norm that is continuous with respect to the C∞-topology, is dominated from above by the L∞-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 pseudonorm that satisfies the aforementioned continuity assumption, is either identically zero or equivalent to Hofer's metric.",
keywords = "22E65, 53D05, 58B20, Hamiltonian diffeomorphisms, Hofer's metric, bi-invariant Finsler metrics",
author = "Lev Buhovsky and Yaron Ostrover",
note = "Funding Information: Acknowledgements. Both authors are grateful to Y. Eliashberg, H. Hofer and L. Polterovich, for their interest in this work and helpful comments and suggestions. Moreover, the authors thank the referee for a careful reading of the text. This article was written during visits of the first author at the Institute for Advanced Study (IAS) in Princeton, and visits of the second author at the Mathematical Sciences Research Institute (MSRI), Berkeley. We thank these institutions for their stimulating working atmospheres and for financial support. The first author was supported by the Mathematical Sciences Research Institute. The second author was supported by NSF Grant DMS-0635607, by a Reintegration Grant SSGHD-268274 within the 7th European Community Framework Programme, and by the Israel Science Foundation grant No. 1057/10.",
year = "2011",
month = dec,
doi = "10.1007/s00039-011-0143-6",
language = "الإنجليزيّة",
volume = "21",
pages = "1296--1330",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "6",
}