Systole growth for finite area hyperbolic surfaces

Florent Balacheff; Eran Makover; Hugo Parlier

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arXiv · 1201.3468

Systole growth for finite area hyperbolic surfaces

Florent Balacheff·Eran Makover·Hugo Parlier

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Abstract

We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$. This maximum is shown to be strictly increasing in terms of the number of cusps for small values of $n$. We also show that this function is greater than a function that grows logarithmically in function of the ratio $g/n$.

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BibTeX RIS

Florent Balacheff, Eran Makover, Hugo Parlier. 2012-09-28. Systole growth for finite area hyperbolic surfaces. https://arxiv.org/abs/1201.3468

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