arXiv Open Access 2024

On the spectral capacity of submanifolds

Dylan Cant Jun Zhang

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.SG

Penulis (2)

Dylan Cant

Jun Zhang

Format Sitasi

APA MLA BibTeX

Cant, D., Zhang, J. (2024). On the spectral capacity of submanifolds. https://arxiv.org/abs/2409.14142

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓