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math.GT2026
Dirichlet domains and the NEC uniformization of extremal hyperbolic surfaces
Ernesto Girondo, Claudia Muñoz
Extremal hyperbolic surfaces are finite-type hyperbolic surfaces that contain an embedded disc of the largest possible radius. We introduce a new general approach to these objects,…
math.GT2023
The minima of the geodesic length functions of uniform filling curves
Ernesto Girondo, Gabino González-Diez, Rubén A. Hidalgo
There is a natural link between (multi-)curves that fill up a closed oriented surface and dessins d'enfants. We use this approach to exhibit explicitly the minima of the geodesic l…