manuscripta mathematica

, Volume 72, Issue 1, pp 251–256

The Schwarz lemma for nonpositively curved Riemmanian surfaces

  • Marc Troyanov

DOI: 10.1007/BF02568278

Cite this article as:
Troyanov, M. Manuscripta Math (1991) 72: 251. doi:10.1007/BF02568278


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.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

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

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