On the spectral capacity of submanifolds
| Autor: | Cant, Dylan, Zhang, Jun |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 29 pages |
| Databáze: | arXiv |
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