The limiting shape of one-dimensional Teichmüller spaces

Sugawa, Toshiyuki

doi:10.1090/S0002-9939-08-09428-8

The limiting shape of one-dimensional Teichmüller spaces
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Proc. Amer. Math. Soc. 136 (2008), 2849-2858 Request permission

Abstract:

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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