The limiting shape of one-dimensional Teichmüller spaces

We show that the Bers embedding of the Teichmüller space of a once-punctured torus converges to the cardioid in the sense of Carathéodory up to rotation when the base torus goes to the boundary of its moduli space.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-08, Vol.136 (8), p.2849-2858
Main Author: Sugawa, Toshiyuki
Format: Article
Language:English
Subjects:
Cardioids
Complex numbers
Conformity
Embeddings
Exact sciences and technology
General mathematics
General, history and biography
Geodesy
Geometric shapes
Mathematical theorems
Mathematics
Perceptron convergence procedure
Riemann surfaces
Sciences and techniques of general use
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Description
Summary:We show that the Bers embedding of the Teichmüller space of a once-punctured torus converges to the cardioid in the sense of Carathéodory up to rotation when the base torus goes to the boundary of its moduli space.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-08-09428-8