Length minima for an infinite family of filling closed curves on a one-holed torus

Zhongzi Wang; Ying Zhang

doi:10.1007/s10711-023-00856-1

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arXiv · 2210.11789

Length minima for an infinite family of filling closed curves on a one-holed torus

Zhongzi Wang·Ying Zhang

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Abstract

We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves, $a^2b^n$ ($n\ge 3$), on a complete one-holed hyperbolic torus in its relative Teichm\"uller space, where $a, b$ are simple closed curves on the one-holed torus which intersect exactly once transversely. This provides concrete examples for the problem to minimize the geodesic length of a fixed filling closed curve on a complete hyperbolic surface of finite type in its relative Teichm\"uller space.

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BibTeX RIS

Zhongzi Wang, Ying Zhang. 2022-10-21. Length minima for an infinite family of filling closed curves on a one-holed torus. https://doi.org/10.1007/s10711-023-00856-1

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