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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 $\partial \Omega$

Topics:
QA

Publisher: Cambridge University Press

Year: 2006

OAI identifier:
oai:wrap.warwick.ac.uk:696

Provided by:
Warwick Research Archives Portal Repository

Downloaded from
http://wrap.warwick.ac.uk/696/1/WRAP_Epsein_Convex_regions.pdf

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