Simple piecewise geodesic interpolation of simple and Jordan curves with applicationsBoedihardjo, 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 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1007/s00365-014-9257-z Abstract/SummaryWe 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.
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