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arXiv · 1409.1813

Minimal rays on surfaces of genus greater than one -- Part II

Jan Philipp Schröder
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Abstract

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 Poincar\'e 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.

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Jan Philipp Schröder. 2014-09-05. Minimal rays on surfaces of genus greater than one -- Part II. https://arxiv.org/abs/1409.1813

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