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arXiv · 2409.14142

On the spectral capacity of submanifolds

Dylan Cant·Jun Zhang
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Abstract

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.

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Dylan Cant, Jun Zhang. 2024-09-21. On the spectral capacity of submanifolds. https://arxiv.org/abs/2409.14142

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