Pleating varieties in the Maskit embeddings of Teichmueller spaces of punctured spheres.

摘要

ood holomorphic coordinates for Teichmuller spaces should be intrinsic, and should be able to reflect the geometry of each surface of the corresponding point in Teichmuller spaces. Maskit's coordinates are intrinsic, and Keen-Series' pleating coordinates for the Maskit embedding of the Teichmuller space of once punctured tori give Maskit's coordinates a geometric interpretation in terms of the geometry of the convex hull boundaries of the groups and their corresponding hyperbolic 3-manifolds.;Pleating loci are parts of the pleating coordinates, which are geodesic laminations on the corresponding surfaces. A pleating variety of a geodesic lamination L is the set of points in the Maskit embedding whose corresponding surfaces have pleating loci L. This paper is concerned with pleating varieties in the Maskit embedding of the Teichmuller space of n times punctured sphere ;Except for some specific cases, it is very difficult to describe pleating varieties explicitly. Instead of describing pleating varieties in an explicit way, the author investigates the asymptotic behavior of pleating varieties in the following way. For every simple closed geodesic