Recent content by hyperttt

can anyone help?

Well, The question I posted is still unsolved. first, thank CompuChip. But what I am asking is the existence of the geodesic in the "homology" class of a given simple closed curve, rather than the existence of the geodesic in the "homotopy" class of a simple closed curve. Can you help? Thanks a...

I am seeking the answer to the following question: Given a simple closed curve on a compact Riemannian surface(a compact surface with a Riemannian metric), whether there exists, in the homology class of this simple closed curve, a (single) closed curve which has the shortest length measured with...