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
Buser,P.: Riemannsche Flächen mit Eigenwerten in (0,1/4), Comment. Math. Helv.52, 25–34 (1977)
Chavel, I., Feldman, E.A.: Cylinders on surfaces, preprint
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Perron, O.: Nichteuklidische Elementargeometrie der Ebene, Stuttgart: Teubner 1962
Randol, B., Cylinders in Riemann surfaces, preprint
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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