A real variable characterization of Gromov hyperbolicity of flute surfaces

2008/05/31 by Ana Portilla, Portilla, Ana, José M. Rodrı́guez +5
Mathematics · #41A10 #46E35 #46G10 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #math.CV #math.MG #msc:41A10 #msc:46E35 #msc:46G10

paper · pdf · doi:10.48550/arxiv.0806.0093

23 pages, 1 latex file, 2 eps figures

arxiv created 2008/05/31 · openalex publication_date 2008/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we give a characterization of the Gromov hyperbolicity of trains (a large class of Denjoy domains which contains the flute surfaces) in terms of the behavior of a real function. This function describes somehow the distances between some remarkable geodesics in the train. This theorem has several consequences; in particular, it allows to deduce a result about stability of hyperbolicity, even though the original surface and the modified one are not quasi-isometric.

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