Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Alex Eskin Committee members: Alex Eskin; Howard Masur.
Özet:
Let (X1, q1) and (X2, q2) be Riemann surfaces with quadratic differentials whose associated flat metrics have unit area and are epsilon-close with respect to a metric built from good systems of period coordinates. Assume X1, X 2 lie over a compact subset K of the moduli space of Riemann surfaces Mg,n. We show that X 1 and X2 are Cepsilon alpha-close in the Teichm¨uller metric. Here, alpha depends only on the genus g and the number of marked points n, while C depends on K. To achieve this, we analyze the uniformization maps of neighborhoods of colliding of singularities of the flat metrics associated to q1 and q2 and build an explicit quasiconformal map between X1 and X2.