Abstract
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 \({n\leq 3}\) .
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The first author was supported in part by SNFS grant number 2100-065270, the second author was supported by SNFS grant number PBEL2-106180.
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Gauglhofer, T., Parlier, H. Minimal length of two intersecting simple closed geodesics. manuscripta math. 122, 321–339 (2007). https://doi.org/10.1007/s00229-006-0071-1
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DOI: https://doi.org/10.1007/s00229-006-0071-1