Systolic inequalities on the sphere from symplectic embeddings
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913885326409728 |
|---|---|
| author | Ferreira, Brayan |
| author_facet | Ferreira, Brayan |
| contents | We use properties of symplectic capacities that were recently defined by Hutchings to obtain upper bounds on the minimal action of Reeb orbits on fiberwise star-shaped hypersurfaces $Σ\subset T^*S^2$. In addition, we introduce the notion of a fiberwise $β$-balanced hypersurface $Σ\subset T^*S^2$ and establish upper bounds for the systole in terms of $β$ and geometric data, in the case of Riemannian metrics on $S^2$ satisfying this property. Finally, under the assumption of antipodal symmetry, we provide a non-sharp estimate of how fiberwise balanced a $δ$-pinched metric is. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Systolic inequalities on the sphere from symplectic embeddings Ferreira, Brayan Symplectic Geometry Differential Geometry 53D25, 53C22 We use properties of symplectic capacities that were recently defined by Hutchings to obtain upper bounds on the minimal action of Reeb orbits on fiberwise star-shaped hypersurfaces $Σ\subset T^*S^2$. In addition, we introduce the notion of a fiberwise $β$-balanced hypersurface $Σ\subset T^*S^2$ and establish upper bounds for the systole in terms of $β$ and geometric data, in the case of Riemannian metrics on $S^2$ satisfying this property. Finally, under the assumption of antipodal symmetry, we provide a non-sharp estimate of how fiberwise balanced a $δ$-pinched metric is. |
| title | Systolic inequalities on the sphere from symplectic embeddings |
| topic | Symplectic Geometry Differential Geometry 53D25, 53C22 |
| url | https://arxiv.org/abs/2506.07674 |