2014/09/05 by Jan Philipp Schröder, Schröder, Jan Philipp
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS
paper · pdf · doi:10.48550/arxiv.1409.1813
3 figures, 20 pages
arxiv created 2014/09/05 · arxiv updated 2014/09/08
We consider any Finsler metric on a closed, orientable surface of genus greater than one. H. M. Morse proved that we can associate an asymptotic direction to minimal rays in the universal cover (in the Poincaré disc: a point on the unit circle). We prove here that, if two minimal rays have a common asymptotic direction, which is not a fixed point of the group of deck transformations, then the two rays can intersect at most in a common initial point. This has strong consequences for the structure of the set of minimal geodesics, as well as for the set of Busemann functions associated to the Finsler metric.