Displaying similar documents to “The hyperbolic metric in a rectangle. II.”

On pairs of closed geodesics on hyperbolic surfaces

Nigel J. E. Pitt (1999)

Annales de l'institut Fourier

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In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups Γ . This links the intersection angles and common perpendiculars of pairs of closed geodesics on Γ / H with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian Δ . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.

Gromov hyperbolicity of planar graphs

Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez (2013)

Open Mathematics

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We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given....

The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry

Oğuzhan Demirel (2009)

Commentationes Mathematicae Universitatis Carolinae

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In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.