Short closed geodesics on cusped hyperbolic surfaces

Thi Hanh Vo

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arXiv · 1912.09967

Short closed geodesics on cusped hyperbolic surfaces

Thi Hanh Vo

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Abstract

This article deals with the set of closed geodesics on complete finite type hyperbolic surfaces. For any non-negative integer $k$, we consider the set of closed geodesics that self-intersect at least $k$ times, and investigate those of minimal length. The main result is that, if the surface has at least one cusp, their self-intersection numbers are exactly $k$ for large enough $k$.

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Thi Hanh Vo. 2019-12-20. Short closed geodesics on cusped hyperbolic surfaces. https://arxiv.org/abs/1912.09967

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