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Hyperbolic lengths and conformal embeddings of Riemann surfaces

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Abstract

Leth be a homeomorphic bijection between hyperbolic Riemann surfacesR andR’. If there is a conformal mapping ofR intoR’ homotopic toh, then for any hyperbolic geodesicc onR the length of the hyperbolic geodesic freely homotopic to the imageh(c) is less than or equal to the hyperbolic length ofc. We show that the converse is not necessarily true.

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Authors and Affiliations

  1. Department of Mathematics, Yamaguchi University, 753-8512, Yamaguchi, Japan

    Makoto Masumoto

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  1. Makoto Masumoto
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Correspondence to Makoto Masumoto.

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Masumoto, M. Hyperbolic lengths and conformal embeddings of Riemann surfaces. Isr. J. Math. 116, 77–92 (2000). https://doi.org/10.1007/BF02773213

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  • DOI: https://doi.org/10.1007/BF02773213

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