A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant

Michael Khanevsky; Fabian Ziltener

doi:10.1016/j.difgeo.2022.101947

A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant

Michael Khanevsky, Fabian Ziltener^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Let (M,ω) be a symplectic manifold and U⊆M an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of U in the compactly supported Hamiltonian group of M. The main result is an upper bound for this map in terms of the Hofer norms for U and M. Applications are upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of U. The first bound is often sharp and the second one is often sharp up to a factor of 2.

Original language	English
Article number	101947
Journal	Differential Geometry and its Application
Volume	85
DOIs	https://doi.org/10.1016/j.difgeo.2022.101947
Publication status	Published - Dec 2022

Keywords

Hofer geometry
Spectral invariants

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1-s2.0-S0926224522001000-mainFinal published version, 530 KBLicence: CC BY

Cite this

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abstract = "Let (M,ω) be a symplectic manifold and U⊆M an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of U in the compactly supported Hamiltonian group of M. The main result is an upper bound for this map in terms of the Hofer norms for U and M. Applications are upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of U. The first bound is often sharp and the second one is often sharp up to a factor of 2.",

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AU - Khanevsky, Michael

AU - Ziltener, Fabian

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N2 - Let (M,ω) be a symplectic manifold and U⊆M an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of U in the compactly supported Hamiltonian group of M. The main result is an upper bound for this map in terms of the Hofer norms for U and M. Applications are upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of U. The first bound is often sharp and the second one is often sharp up to a factor of 2.

AB - Let (M,ω) be a symplectic manifold and U⊆M an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of U in the compactly supported Hamiltonian group of M. The main result is an upper bound for this map in terms of the Hofer norms for U and M. Applications are upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of U. The first bound is often sharp and the second one is often sharp up to a factor of 2.

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KW - Spectral invariants

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A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant

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Keywords

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