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Systole growth for finite area hyperbolic surfaces

Florent Balacheff; Eran Makover; Hugo Parlier — 2014

Annales de la faculté des sciences de Toulouse Mathématiques

In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g, n)$ is greater than a function that grows logarithmically in terms of the ratio $g / n$ .

The first eigenvalue of a Riemann surface.

Brooks, Robert; Makover, Eran — 1999

Electronic Research Announcements of the American Mathematical Society [electronic only]

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