Hyperbolic elliptic parabolic disks approximated by half distance bands

2026/03/09 by Gyula Lakos · 1 voice
Mathematics · #math.HO #math.MG

paper · pdf

Abstract

Hyperbolic elliptic parabolic disks can be described by the inequality (x²)/(C²)+2y²-2y≤0 (0<C<1) in the unit disk based Beltrami--Cayley--Klein model of the hyperbolic geometry, up to hyperbolic congruences. The hyperbolic elliptic parabolic disks considered above are sort of close to their supporting half distance bands given by the inequalities (x²)/(C²)+ y²-1≤0 and y≥0. Here we consider what `close' might mean, and we look for even more precise approximations, in terms of area and circumference.

Citations

• Spherical and hyperbolic conics
• Spherical, hyperbolic and other projective geometries: convexity, duality, transitions
• Constructive curves in non-Euclidean planes
• Isoptic curves of generalized conic sections in the hyperbolic plane
• A Geometrical Background for De Sitter's World
• Théorie des groupes fuchsiens

Discussions

• Gyula Lakos: Hyperbolic elliptic parabolic disks approximated by half distance bands https://arxiv.org/abs/2603.08226 https://arxiv.org/pdf/2603.08226 https://arxiv.org/html/2603.08226 [bsky, 0 points, 0 comments]

Related

• Mobile disks in hyperbolic space and minimization of conformal capacity
• Analytic mappings of the unit disk which almost preserve hyperbolic area
• Subelliptic Li-Yau estimates on three dimensional model spaces
• Two moons in a puddle
• A short proof of a conjecture of Aougab-Huang