Geometric filling curves on punctured surfaces


 This paper is about a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly truncated orthogeodesic that are 
 
 
 
$\varepsilon$

 
 -dense on a given compact set on the surface.