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CRITICAL EXPONENT OF NEGATIVELY CURVED THREE MANIFOLDS

Published online by Cambridge University Press:  31 July 2003

YONG HOU
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419, U.S.A. e-mail: yhou@math.uiowa.edu
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Abstract

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We prove that for a negatively pinched ($-b^2\le\cK\le -1$) topologically tame 3-manifold $\skew5\tilde{M}/\Gamma$, all geometrically infinite ends are simply degenerate. And if the limit set of $\Gamma$ is the entire boundary sphere at infinity, then the action of $\Gamma$ on the boundary sphere is ergodic with respect to harmonic measure, and the Poincaré series diverges when the critical exponent is 2.

Keywords

Type
Research Article
Copyright
2003 Glasgow Mathematical Journal Trust