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The Schwarz lemma for nonpositively curved Riemmanian surfaces

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Abstract

In this paper, we prove that if f is a conformal map between two Riemannian surfaces, and if the curvature of the target is nonpositive and less than or equal to the curvature of the source, then the map is contracting.

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Authors and Affiliations

  1. Département de Mathématiques, Université du Québec à Montreal, Succursale A, C.P. 8888, H3C 3P8, Montréal, (Québec), Canada

    Marc Troyanov

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  1. Marc Troyanov
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Troyanov, M. The Schwarz lemma for nonpositively curved Riemmanian surfaces. Manuscripta Math 72, 251–256 (1991). https://doi.org/10.1007/BF02568278

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  • DOI: https://doi.org/10.1007/BF02568278

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