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Cusps are dense. (English) Zbl 0718.30033
In this remarkable paper it is shown that maximal cusps are dense in Bers’ boundary for Teichmüller space. The density of cusps was conjectured by Bers in 1970. The proof rests on an estimate for the algebraic change in a quasifuchsian group due to the unit quasiconformal deformation concentrated in the thin part of the quotient Riemann surface. A maximal cusp is uniquely determined by the system of simple closed curves which is pinched. Hence the result is a first step towards a combinatorial description of the boundary.

30F60 Teichmüller theory for Riemann surfaces
32G05 Deformations of complex structures
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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