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June 1996 Compact Quotient Manifolds of Domains in a Complex 3-Dimensional Projective Space and the Lebesgue Measure of Limit Sets
Masahide KATO
Tokyo J. Math. 19(1): 99-119 (June 1996). DOI: 10.3836/tjm/1270043222

Abstract

We shall consider compact complex manifolds of dimension three which have subdomains in a three dimensional projective space as their unramified even coverings. Assume that the subdomains contain projective lines. Then any pair of such manifolds can be connected together complex analytically by an analogue of Klein combinations [K1]. In this paper, we shall prove a (weak) analogue of two results of B. Maskit [M] on the Lebesgue measures of the limit set of Kleinian groups (Theorems A and B). In section 1, we shall give definitions of terms and precise statement of our result. In section 2, we shall analyze the limit set by the same method as that of Maskit. Section 3 is devoted to proving Theorem 2.1. As a corollary to Theorem 2.1, we obtain Theorem A, which is an analogue of Combination Theorem I of [M]. In section 4, we shall prove Theorem B, which is an analogue of Combination Theorem II of [M].

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Masahide KATO. "Compact Quotient Manifolds of Domains in a Complex 3-Dimensional Projective Space and the Lebesgue Measure of Limit Sets." Tokyo J. Math. 19 (1) 99 - 119, June 1996. https://doi.org/10.3836/tjm/1270043222

Information

Published: June 1996
First available in Project Euclid: 31 March 2010

zbMATH: 0864.57034
MathSciNet: MR1391931
Digital Object Identifier: 10.3836/tjm/1270043222

Rights: Copyright © 1996 Publication Committee for the Tokyo Journal of Mathematics

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Vol.19 • No. 1 • June 1996
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