EARTHQUAKES ON RIEMANN SURFACES AND ON MEASURED GEODESIC LAMINATIONS

Let S be a closed orientable surface of genus ar least 2. We study pro perties of its Teichmuller space T(S), namely of the space of isotopy classes of conformal structures on S. W. P. Thurston introduced a cert ain compactification of T(S) by what he called the space of projective measured geodesic laminations. He also introduced some transformation s of Teichmuller space, called earthquakes, which are intimately relat ed to the geometry of T(S) . A general problem is to understand which geometric properties of Teichmuller space subsist at infinity, on Thur ston's boundary. In particular, it is natural to ask whether earthquak es continuously extend at certain points of Thurston's boundary, and a t precisely which points they do so. This is the principal question ad dressed in this paper.