Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications
Classical Analysis and ODEs
2014-07-18 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1309.1576,
title = {Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications},
author = {Horatio Boedihardjo and Xi Geng},
journal= {arXiv preprint arXiv:1309.1576},
year = {2014}
}
Comments
20 pages, 5 figures