Institute for Mathematical Sciences
Cusps in complex boundaries of one-dimensional Teichm\"uller space.
Abstract: This paper gives a proof of the conjectural phenomena on the complex boundary one-dimensional slices: Every rational
boundary point is cusp shaped. This paper treats this problem
for Bers slices, the Earle slices, and the Maskit slice.
In proving this, we also obtain the following result: Every
Teichm\"uller modular transformation acting on a Bers slice
can be extended as a quasi-conformal mapping on its ambient
space. We will observe some similarity phenomena on the
boundary of Bers slices, and discuss on the dictionary
between Kleinian groups and Rational maps concerning with
these phenomena. We will also give a result related to the
theory of L.Keen and C.Series of pleated varieties in
quasifuchsian space of once punctured tori.
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