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

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)

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.

KW - Hofer geometry

KW - Spectral invariants

UR - https://www.scopus.com/pages/publications/85138595276

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DO - 10.1016/j.difgeo.2022.101947

M3 - Article

AN - SCOPUS:85138595276

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JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

M1 - 101947

ER -

A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant

Abstract

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Keywords

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