LAUSR

ABSTRACT We can shorten any path that links two given points by applying short ruler transforms iteratively. In this article we take a closer look at a short ruler process on the torus. The torus is a compact Riemannian manifold and at least a subsequence of the process converges to a geodesic between the two points. However, on compact Riemann manifolds there might exist different limit geodesics (with the same length). On the torus, the geodesics with the same length are isolated and the limit geodesic is unique.