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Minimal length of nonsimple closed geodesics on hyperbolic surfaces

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arxiv 2207.08360 v1 pith:GP7V6L6U submitted 2022-07-18 math.GT

Wujie Shen , Jiajun Wang This is my paper · ORCID
classification math.GT
keywords closedgeodesicshyperboliclengthminimalsurfacesfinite-typegets
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abstract

In the present paper, we show that the minimal length of closed geodesics on finite-type hyperbolic surfaces with self-intersection number $k$ has order $2\log k$ as $k$ gets large.

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  1. Shortest filling geodesics on hyperbolic surfaces

    math.GT 2025-06 conditional novelty 7.0 of 10

    A filling multi-geodesic on a genus g hyperbolic surface has length at least half the perimeter of a regular right-angled (8g-4)-gon, and this bound is sharp.

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