Duke Mathematical Journal

The conformal boundary and the boundary of the convex core

R. D. Canary

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Abstract

In this note we investigate the relationship between the conformal boundary at infinity of a hyperbolic 3-manifold and the boundary of its convex core. In particular, we prove that the length of a curve in the conformal boundary gives an upper bound on the length of the corresponding curve in the boundary of the convex core.

Article information

Source
Duke Math. J. Volume 106, Number 1 (2001), 193-207.

Dates
First available in Project Euclid: 13 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1092403892

Mathematical Reviews number (MathSciNet)
MR1810370

Digital Object Identifier
doi:10.1215/S0012-7094-01-10616-9

Zentralblatt MATH identifier
1012.57021

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 30F40: Kleinian groups [See also 20H10] 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)

Citation

Canary, R. D. The conformal boundary and the boundary of the convex core. Duke Mathematical Journal 106 (2001), no. 1, 193--207. doi:10.1215/S0012-7094-01-10616-9. http://projecteuclid.org/euclid.dmj/1092403892.


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