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
- Authors
- Amorim, Lino; Oh, Yong-geun; Dos Santos, Joana Oliveira
- Date Issued
- 2018-11
- 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 Mane sets of a Tonelli Hamiltonian and to generalise a result of Arnaud on Lagrangians invariant under the flow of such Hamiltonians.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/95501
- DOI
- 10.1017/S0305004117000561
- ISSN
- 0305-0041
- Article Type
- Article
- Citation
- MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 165, no. 3, page. 411 - 434, 2018-11
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