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, Volume 72, Issue 1, pp 251–256 | Cite as

The Schwarz lemma for nonpositively curved Riemmanian surfaces

  • Marc Troyanov


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.


Riemannian Surface Conical Singularity Schwarz Lemma Open Riemann Surface Generalize Maximum Principle 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Marc Troyanov
    • 1
  1. 1.Département de MathématiquesUniversité du Québec à MontrealMontréalCanada

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