In this paper we study the geodesics and ends of compact surfaces satisfying the "uniform visibility" axiom. We are primarily though not exclusively interested in finitely connected surfaces, which topologically are compact Riemann surfaces with a finite number of punctures.
We study the behavior of maximal geodesics outside a sufficiently large compact set in a finitely connected, complete and noncompact 2-dimensional Riemannian manifold (possibly with boundary). One of our main results states that if the total curvature of [italic]M exists and is …
A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [italic capital]E on [italic capital]M, and a Riemannian metric [italic capital]G on [italic capital]E. All length-minimiz…