Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces

Abstract

Let S and R be two hyperbolic finite area surfaces with cusps. We show that for every є > 0 there are finite degree unbranched covers Sє → S and Rє → R, such that the Weil-Petersson distance between Sє and Rє is less than є in the corresponding Moduli space.

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