%0 Journal Article
%T Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications
%A Horatio Boedihardjo
%A Xi Geng
%J Mathematics
%D 2013
%I arXiv
%X We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green's theorem and the uniqueness of signature for planar Jordan curves with finite p-variation for 1<=p<2.
%U http://arxiv.org/abs/1309.1576v2