Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains
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_ | 1866910921832529920 |
|---|---|
| author | Fletcher, Alastair Hahn, Allyson |
| author_facet | Fletcher, Alastair Hahn, Allyson |
| contents | Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that quasiconformality and quasisymmetry with respect to the quasihyperbolic metric are equivalent. The second is to study normal quasiregular maps from such a domain into $S^n$ or $\mathbb{R}^n$ and show they enjoy geometric properties such as a uniform Hölder condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains Fletcher, Alastair Hahn, Allyson Complex Variables Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that quasiconformality and quasisymmetry with respect to the quasihyperbolic metric are equivalent. The second is to study normal quasiregular maps from such a domain into $S^n$ or $\mathbb{R}^n$ and show they enjoy geometric properties such as a uniform Hölder condition. |
| title | Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2504.20806 |