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Weil-Petersson Areas of The Moduli Spaces Of Tori

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Abstract

We study the Teichmüller spaces of torus with one branch point of order v and of torus with a totally geodesic boundary curve of length m, respectively. Applying the obtained results for the corresponding moduli spaces we find that the Weil-Petersson area of the moduli space of torus with one conical point of order v is (π2/6)(1 - l/v2) and that of the moduli space of torus with a totally geodesic boundary curve of length m is π2/6 + m2/24.

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Authors and Affiliations

  1. Department of Mathematics, University of Helsinki P]Finland, P.O. Box 4 (Yliopistonkatu 5), FIN-00014

    Marjatta Näätänen

  2. Graduate School of Polymathematics Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-01, Japan

    Toshihiro Nakanishi

Authors
  1. Marjatta Näätänen
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  2. Toshihiro Nakanishi
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Correspondence to Marjatta Näätänen.

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Näätänen, M., Nakanishi, T. Weil-Petersson Areas of The Moduli Spaces Of Tori. Results. Math. 33, 120–133 (1998). https://doi.org/10.1007/BF03322076

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