The conformal boundary and the boundary of the convex core
# The conformal boundary and the boundary of the convex core

### R.D. Canary^{1}

### Department of Mathematics, University of Michigan,
Ann Arbor, MI 48109

## 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.

### Footnotes:

^{1}Research
supported in part by grants from the National Science Foundation

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On 27 Nov 1999, 12:50.