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Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry-Mather theory

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Title
Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry-Mather theory
Author(s)
Lino Amorim; Yong-Geun Oh; Joana Oliveira Dos Santos
Publication Date
2018-11
Journal
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v.165, no.3, pp.411 - 434
Publisher
CAMBRIDGE UNIV PRESS
Abstract
We construct graph selectors for compact exact Lagrangians in the cotangent bundle of an orientable, closed manifold. The construction combines Lagrangian spectral invariants, developed by Oh, and results, by Abouzaid, about the Fukaya category of a cotangent bundle. We also introduce the notion of Lipschitz-exact Lagrangians and prove that these admit an appropriate generalisation of graph selector. We then, following Bernard–Oliveira dos Santos, use these results to give a new characterisation of the Aubry and Ma˜ n´e sets of a Tonelli Hamiltonian and to generalise a result of Arnaud on Lagrangians invariant under the flow of such Hamiltonians. (c) Cambridge Philosophical Society 2017
URI
https://pr.ibs.re.kr/handle/8788114/4269
ISSN
0305-0041
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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2017_YGO_exact_lagrangian_submanifolds_lagrangian_spectral_invariants_and_aubrymather_theory.pdfDownload

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