On the spectral capacity of submanifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929509660360704 |
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| author | Cant, Dylan Zhang, Jun |
| author_facet | Cant, Dylan Zhang, Jun |
| contents | The infimum of the spectral capacities of neighbourhoods of a nowhere coisotropic submanifold is shown to be zero. In contrast, neighbourhoods of a closed Lagrangian submanifold, and of certain contact-type hypersurfaces, are shown to have uniformly positive spectral capacity. Along the way we prove a quantitative Lagrangian control estimate relating spectral invariants, boundary depth, and the minimal area of holomorphic disks. The Lagrangian control also provides novel obstructions to certain Lagrangian embeddings into a symplectic ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the spectral capacity of submanifolds Cant, Dylan Zhang, Jun Symplectic Geometry 53D40, 53D12 The infimum of the spectral capacities of neighbourhoods of a nowhere coisotropic submanifold is shown to be zero. In contrast, neighbourhoods of a closed Lagrangian submanifold, and of certain contact-type hypersurfaces, are shown to have uniformly positive spectral capacity. Along the way we prove a quantitative Lagrangian control estimate relating spectral invariants, boundary depth, and the minimal area of holomorphic disks. The Lagrangian control also provides novel obstructions to certain Lagrangian embeddings into a symplectic ball. |
| title | On the spectral capacity of submanifolds |
| topic | Symplectic Geometry 53D40, 53D12 |
| url | https://arxiv.org/abs/2409.14142 |