Minimal measured laminations in geometric 3-manifolds

Ken’ichi Ohshika

Vol. 144 (1990), No. 2, 327–344

DOI: 10.2140/pjm.1990.144.327

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 R^𝒮 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