Convex iso-Delaunay regions in strata of translation surfaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912602305593344 |
|---|---|
| author | Freedman, Sam Zykoski, Bradley |
| author_facet | Freedman, Sam Zykoski, Bradley |
| contents | Strata of translation surfaces are covered by the closures of finitely many iso-Delaunay regions: open subspaces parametrizing surfaces whose Delaunay triangulations are combinatorially equivalent. We prove that the iso-Delaunay regions for triangulations with involutions called triangle matchings are convex with respect to the angle coordinates of the triangles. As a corollary, we show that all iso-Delaunay regions in hyperelliptic stratum components are convex. This work generalizes two directions in the theory of flat surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convex iso-Delaunay regions in strata of translation surfaces Freedman, Sam Zykoski, Bradley Geometric Topology Dynamical Systems Primary: 32G15, Secondary: 30F30, 57M50 Strata of translation surfaces are covered by the closures of finitely many iso-Delaunay regions: open subspaces parametrizing surfaces whose Delaunay triangulations are combinatorially equivalent. We prove that the iso-Delaunay regions for triangulations with involutions called triangle matchings are convex with respect to the angle coordinates of the triangles. As a corollary, we show that all iso-Delaunay regions in hyperelliptic stratum components are convex. This work generalizes two directions in the theory of flat surfaces. |
| title | Convex iso-Delaunay regions in strata of translation surfaces |
| topic | Geometric Topology Dynamical Systems Primary: 32G15, Secondary: 30F30, 57M50 |
| url | https://arxiv.org/abs/2509.19550 |