Simple piecewise geodesic interpolation of simple and Jordan curves with applications

Boedihardjo, H. and Geng, X. (2015) Simple piecewise geodesic interpolation of simple and Jordan curves with applications. Constructive Approximation, 42 (1). pp. 161-180. ISSN 1432-0940 doi: 10.1007/s00365-014-9257-z

Abstract/Summary

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.