Epstein, D. B. A., Marden, A. and Markovic, V. (Vladimir) (2006) Convex regions in the plane and their domes. Proceedings of the London Mathematical Society, Vol.92 (No.3). pp. 624-654. doi:10.1017/S002461150501573X ISSN 0024-6115 .

Preview

PDF WRAP_Epsein_Convex_regions.pdf - Requires a PDF viewer. Download (351Kb)

Request Changes to record.

Abstract

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 $\partial \Omega$.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Convex domains, Convex geometry, Geometry, Hyperbolic, Geometry, Plane, Algebraic number theory
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6115
Official Date:	May 2006
Dates:	Date Event May 2006 Published
Volume:	Vol.92
Number:	No.3
Page Range:	pp. 624-654
DOI:	10.1017/S002461150501573X
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads