Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Convergence of refinement schemes on metric spaces

Author: Oliver Ebner
Journal: Proc. Amer. Math. Soc. 141 (2013), 677-686
MSC (2010): Primary 53C23, 65D17
Published electronically: June 7, 2012
MathSciNet review: 2996972
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Abstract: We analyze the convergence of iterative refinement processes on metric spaces, imposing the principle of contractivity to obtain convergence criteria. As a major result, we show that on Hadamard spaces a wide natural class of contractible barycentric subdivision schemes converges.

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Oliver Ebner
Affiliation: Institute of Geometry, TU Graz, Kopernikusgasse 24/IV, A-8010 Graz, Austria

Keywords: Hadamard space, barycentric subdivision scheme
Received by editor(s): March 25, 2011
Received by editor(s) in revised form: June 30, 2011
Published electronically: June 7, 2012
Additional Notes: The author was supported by the Austrian science fund, grant W1230.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.