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The collar theorem and examples

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Abstract

We generalize Randol's estimate of the length of cylinders in Riemann surfaces to arbitrary variable curvature and give examples with constant curvature to show that the bound is sharp.

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References

  1. Buser,P.: Riemannsche Flächen mit Eigenwerten in (0,1/4), Comment. Math. Helv.52, 25–34 (1977)

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  2. Chavel, I., Feldman, E.A.: Cylinders on surfaces, preprint

  3. Cheeger, J., Ebin, D.G.: Comparison theorems in Riemannian geometry, Amsterdam: North Holland 1975

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  4. Perron, O.: Nichteuklidische Elementargeometrie der Ebene, Stuttgart: Teubner 1962

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  5. Randol, B., Cylinders in Riemann surfaces, preprint

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Authors and Affiliations

  1. Sonderforschungsbereich 40 Mathematisches Institut, Universität Bonn, Wegelerstrasse 10, D-53, Bonn, Germany

    Peter Buser

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  1. Peter Buser
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Written at Sonderforschungsbereich 40, University of Bonn.

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Buser, P. The collar theorem and examples. Manuscripta Math 25, 349–357 (1978). https://doi.org/10.1007/BF01168048

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  • DOI: https://doi.org/10.1007/BF01168048

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