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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

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To link to this item 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:42382
Publisher:Springer

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