| Let S be a closed orientable surface with genus g ≥ 2. Let T (S) be the Teichmuller space and C (S) the complex of curves. We write PML (S) to denote the Thurston boundary of T (S), and 6infinityC (S) to denote the Gromov boundary of C (S). Let UML (S) be the quotient space of PML (S) by forgetting measure with the quotient map u. Let L be a fixed Bers constant. For sigma ∈ T (S), let phi(sigma) be a pants decomposition whose total length is bounded by L, where all pants curves are geodesics in sigma. Suppose that sigmai ∈ T (S) converges to [ l ] ∈ PML (S). Consider the decomposition ul =l1∪l2 ∪&cdots;∪lm as a finite disjoint union of minimal laminations. Suppose that alphai is a pants curve in phi(sigma i). In this thesis we show: (1) If phi(sigma i) converges to a geodesic lamination nu in Hausdorff metric topology, then u([ l ]) ⊂ nu. (2) Suppose that l1 is a simple closed curve. Consider an annular covering Y of S in which a neighborhood of l1 lifts homeo-morphically. Suppose that alpha i meets l1 for all i. Then the absolute value of algebraic intersection number |a1 · ai| approaches to infinity, where a1 is a lift of alpha 1 which connects the two boundaries of Y and so is ai. (3) Suppose that l2 is not a simple closed curve. Let F be the essential subsurface of S which is filled by l2 Let bi be a component of alphai ∩ F. We can define a simple closed curve b&d5;i from bi in a canonical way. Then the geodesic representative of b&d5;i converges to l2 in UML (F). (4) In particular, if l is a filling lamination then alphai converges to u([ l ]) in C (S) ∪ 6infinityC (S), where u([ l ]) is considered as an element of 6infinityC (S). |
