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Simple piecewise geodesic interpolation of simple and Jordan curves with applications
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Boedihardjo, Horatio and Geng, Xi (2014) Simple piecewise geodesic interpolation of simple and Jordan curves with applications. Constructive Approximation, 42 (1). pp. 161-180. doi:10.1007/s00365-014-9257-z ISSN 1432-0940.
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Official URL: https://doi.org/10.1007/s00365-014-9257-z
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.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Constructive Approximation | ||||||
Publisher: | Springer | ||||||
ISSN: | 1432-0940 | ||||||
Official Date: | 13 August 2014 | ||||||
Dates: |
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Volume: | 42 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 161-180 | ||||||
DOI: | 10.1007/s00365-014-9257-z | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Funder: | European Research Council | ||||||
Grant number: | 291244 | ||||||
Open Access Version: |
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