Uniqueness of maximal inscribed parabolas and minimal circumscribing horocycles

Lukarevski, Martin and Schröcker, Hans-Peter (2026) Uniqueness of maximal inscribed parabolas and minimal circumscribing horocycles. Advances in Geometry, 26 (3). ISSN 1615-715X

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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.

Item Type: Article
Subjects: Natural sciences > Matematics
Divisions: Faculty of Computer Science
Depositing User: Martin Lukarevski
Date Deposited: 16 Sep 2026 08:18
Last Modified: 16 Sep 2026 08:18
URI: https://eprints.ugd.edu.mk/id/eprint/39043

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