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CRITICAL EXPONENT OF NEGATIVELY CURVED THREE MANIFOLDS

Published online by Cambridge University Press:  31 July 2003

YONG HOU
YONG HOU
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419, U.S.A. e-mail: [email protected]
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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

57M5057M60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 373 - 387
Copyright
2003 Glasgow Mathematical Journal Trust