Convex regions in the plane and their domes

• Autores: D.B.A. Epstein, A. Marden, V. Markovic
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 92, Nº 3, 2006, págs. 624-654
• Idioma: inglés
• DOI: 10.1017/s002461150501573x
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• Resumen

  • We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2-quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$.