I wonder how difficult it is to compute geodesics on Dini's Surface, a twisted pseudosphere? Here is one parametrization, from Alfred Gray's Modern Differential Geometry of Curves and Surfaces, ...
Let $A(S)$ denotes the Arc complex of a finite type hyperbolic surface $S$ with nonempty boundary. Let $\lambda:A(S)\rightarrow A(S)$ be a map such that on triangulations of $S$ i.e. on the top ...
A Theorem by Gallo, Goldman and Porter states the following: Let $S_g$ be a closed orientable surface of genus $g$ with fundamental group $\Gamma_g$, and fix a non-elementary representation ...
Let $S$ be a closed surface of genus $g \geq 2$. There exist two simple closed curves filling $S$? Definitions: Two closed curves $\alpha, \beta$ fill $S$ if they have minimal intersection and $S ...