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Space filling curves and geodesic laminations

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Abstract

In this paper we study a class of connected fractals that admit a space filling curve. We prove that these curves are Hölder continuous and measure preserving. To these space filling curves we associate geodesic laminations satisfying among other properties that points joined by geodesics have the same image in the fractal under the space filling curve. The laminations help us to understand the geometry of the curves. We define an expanding dynamical system on the laminations.

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  1. Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas, 1086, Venezuela

    Víctor F. Sirvent

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  1. Víctor F. Sirvent
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Correspondence to Víctor F. Sirvent.

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Sirvent, V.F. Space filling curves and geodesic laminations. Geom Dedicata 135, 1–14 (2008). https://doi.org/10.1007/s10711-008-9253-1

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  • DOI: https://doi.org/10.1007/s10711-008-9253-1

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