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Minimal length of two intersecting simple closed geodesics

Gauglhofer, Thomas ; Parlier, Hugo

In: manuscripta mathematica, 2007, vol. 122, no. 3, p. 321-339

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    Title
    • Minimal length of two intersecting simple closed geodesics
    Author
    • Gauglhofer, Thomas. Section de Mathématiques, EPFL, 1015, Switzerland, Lausanne
    • Parlier, Hugo. Section de Mathématiques, Université de Genève, 1211, Genève, Switzerland
    Document Type
    • Postprint
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:317142
    Summary
    On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we address the question of a sharp lower bound L n on the length attained by the longest of the two geodesics. We show the existence of a surface S n on which there exists two simple closed geodesics of length L n intersecting n times and explicitly find L n for $${n\leq 3}$$