The geometry of Euclidean surfaces with conical singularities
arXiv:1306.1759
Abstract
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points. Dynamical properties for the space of geodesics are also proved.
18 pages, 1 figure