Uniqueness of maximal inscribed parabolas and minimal circumscribing horocycles
Abstract
Abstract We prove existence of three unique “max-exparabolas” to a triangle. Each of these parabolas is internally tangent to one edge and the two other sides. Among all like parabolas, it is characterized by having maximal parameter. We use this result to prove a more general uniqueness statement on maximal parabolas in a convex point set. In similar spirit, we demonstrate uniqueness of minimal enclosing horocycles in hyperbolic geometry, provided the enclosed set is sufficiently small.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematics and Applications
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Advances in Geometry
- Publisher
- Walter de Gruyter GmbH
- Volume
- 26
- Issue
- 3
- Pages
- 303–312
- Publication date
- 21 March 2026
- Language
- EN