大鹿 健一

In this paper we deal with codimension-1 measured laminations whose leaves are minimal surfaces in geometric 3-manifolds with either SL2R or H 2 × 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 Ry 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. © 1990 by Pacific Journal of Mathematics.