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September 2017 Hamiltonian C0-continuity of Lagrangian capacity on the cotangent bundle
Yong-Geun Oh
Kyoto J. Math. 57(3): 613-636 (September 2017). DOI: 10.1215/21562261-2017-0008

Abstract

Partially motivated by the study of topological Hamiltonian dynamics, we prove the following C0-continuity of the Lagrangian capacity function γlag:

γlag(ϕH1(oN)):=ρlag(H;1)ρlag(H;[pt]#)0, as ϕH1id, provided the H’s satisfy suppXHDR(TN)oB for some R>0 and a closed subset BN with nonempty interior. We also provide an estimate of the capacity in terms of the C0-distance of dC0(ϕH1,id) and the subset BN relative to TN.

Citation

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Yong-Geun Oh. "Hamiltonian C0-continuity of Lagrangian capacity on the cotangent bundle." Kyoto J. Math. 57 (3) 613 - 636, September 2017. https://doi.org/10.1215/21562261-2017-0008

Information

Received: 25 June 2013; Revised: 9 February 2015; Accepted: 2 May 2016; Published: September 2017
First available in Project Euclid: 22 April 2017

zbMATH: 1378.53090
MathSciNet: MR3685057
Digital Object Identifier: 10.1215/21562261-2017-0008

Subjects:
Primary: 53D05
Secondary: 28D10, 53D35, 53D40

Rights: Copyright © 2017 Kyoto University

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Vol.57 • No. 3 • September 2017
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