Power with Respect to Generalized Spheres and Radical Surfaces in $\mathbf{H}^n$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912894403215360 |
|---|---|
| author | Világi, Áron Szirmai, Jenő |
| author_facet | Világi, Áron Szirmai, Jenő |
| contents | This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we derive a novel formula for hyperspheres and also prove that the radical surface of any two non-concentric generalized spheres is a hyperplane. These results provide tools for constructing power diagrams and studying hyperball packings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Power with Respect to Generalized Spheres and Radical Surfaces in $\mathbf{H}^n$ Világi, Áron Szirmai, Jenő Metric Geometry 51M10, 51M15, 52A20, 52C17, 52C22, 52B15 This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we derive a novel formula for hyperspheres and also prove that the radical surface of any two non-concentric generalized spheres is a hyperplane. These results provide tools for constructing power diagrams and studying hyperball packings. |
| title | Power with Respect to Generalized Spheres and Radical Surfaces in $\mathbf{H}^n$ |
| topic | Metric Geometry 51M10, 51M15, 52A20, 52C17, 52C22, 52B15 |
| url | https://arxiv.org/abs/2602.09698 |