Compact non-orientable hyperbolic surfaces with an extremal metric disc

Girondo, Ernesto; Nakamura, Gou

doi:10.1090/S1088-4173-07-00157-9

Compact non-orientable hyperbolic surfaces with an extremal metric disc
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by Ernesto Girondo and Gou Nakamura PDF

Conform. Geom. Dyn. 11 (2007), 29-43 Request permission

Abstract:

The size of a metric disc embedded in a compact non-orientable hyperbolic surface is bounded by some constant depending only on the genus $g \ge 3$. We show that a surface of genus greater than six contains at most one metric disc of the largest radius. For the case $g=3$, we carry out an exhaustive study of all the extremal surfaces, finding the location of every extremal disc inside them.

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