Vol. 144, No. 2, 1990

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Minimal measured laminations in geometric 3-manifolds

Ken’ichi Ohshika

Vol. 144 (1990), No. 2, 327–344
Abstract

In this paper we deal with codimension-1 measured laminations whose leaves are minimal surfaces in geometric 3-manifolds with either SL2R or H2 × E structures. We call such measured laminations minimal measured laminations. Our main theorem states that in a geometric 3-manifold with an SL2R-structure every class in R𝒮 containing incompressible measured laminations is represented uniquely by a minimal measured lamination. This implies that every incompressible lamination in such a 3-manifold is equivalent to a unique minimal measured lamination, which is vertical with respect to geometric fibering structure.

Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57R30
Milestones
Received: 18 October 1988
Revised: 8 May 1989
Published: 1 August 1990
Authors
Ken’ichi Ohshika
Department of Mathematics, Graduate School of Science
Osaka University
Toyonaka
Osaka 560-0043
Japan