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Coisotropic Ekeland–Hofer capacities

Part of: Hamiltonian and Lagrangian mechanics Global differential geometry Differential topology Symplectic geometry, contact geometry

Published online by Cambridge University Press:  05 September 2022

Rongrong Jin  and
Guangcun Lu
Rongrong Jin
Affiliation:
Department of Mathematics, Civil Aviation University of China, Tianjin 300300, The People's Republic of China (rrjin@cauc.edu.cn)
Guangcun Lu*
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, The People's Republic of China (gclu@bnu.edu.cn)
*
*Corresponding author
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Abstract

For subsets in the standard symplectic space $(\mathbb {R}^{2n},\omega _0)$ whose closures are intersecting with coisotropic subspace $\mathbb {R}^{n,k}$ we construct relative versions of the Ekeland–Hofer capacities of the subsets with respect to $\mathbb {R}^{n,k}$, establish representation formulas for such capacities of bounded convex domains intersecting with $\mathbb {R}^{n,k}$. We also prove a product formula and a fact that the value of this capacity on a hypersurface $\mathcal {S}$ of restricted contact type containing the origin is equal to the action of a generalized leafwise chord on $\mathcal {S}$.

Keywords

Symplectic invariantEkeland–Hofer capacitiescoisotropic

MSC classification

Primary: 53D35: Global theory of symplectic and contact manifolds 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 70H05: Hamilton's equations 57R17: Symplectic and contact topology

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 5 , October 2023 , pp. 1564 - 1608
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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