Packing stability and the subleading asymptotics of symplectic Weyl laws
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912594432884736 |
|---|---|
| author | Edtmair, Oliver |
| author_facet | Edtmair, Oliver |
| contents | We prove that symplectic ball packing stability holds for every compact, connected symplectic $4$-manifold with smooth boundary. This follows from a stronger result: the full volume of any such manifold can be filled by a single symplectic ellipsoid. As an application, we obtain estimates - with sharp exponents - for the error terms in the symplectic Weyl laws for embedded contact homology capacities, periodic Floer homology spectral invariants, and link spectral invariants. We also construct an example of a star-shaped domain in $\mathbb{R}^4$, arbitrarily $C^1$ close to the unit ball and with boundary of regularity just below $C^2$ and smooth away from a single point, for which packing stability fails. Our proofs reveal a close connection between symplectic packing stability in the presence of smooth boundary and the algebraic structure of Hamiltonian diffeomorphism groups, particularly Banyaga's simplicity results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Packing stability and the subleading asymptotics of symplectic Weyl laws Edtmair, Oliver Symplectic Geometry We prove that symplectic ball packing stability holds for every compact, connected symplectic $4$-manifold with smooth boundary. This follows from a stronger result: the full volume of any such manifold can be filled by a single symplectic ellipsoid. As an application, we obtain estimates - with sharp exponents - for the error terms in the symplectic Weyl laws for embedded contact homology capacities, periodic Floer homology spectral invariants, and link spectral invariants. We also construct an example of a star-shaped domain in $\mathbb{R}^4$, arbitrarily $C^1$ close to the unit ball and with boundary of regularity just below $C^2$ and smooth away from a single point, for which packing stability fails. Our proofs reveal a close connection between symplectic packing stability in the presence of smooth boundary and the algebraic structure of Hamiltonian diffeomorphism groups, particularly Banyaga's simplicity results. |
| title | Packing stability and the subleading asymptotics of symplectic Weyl laws |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2509.15390 |