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Axioms 2012, 1(2), 99-110; doi:10.3390/axioms1020099
Article

Fat Triangulations, Curvature and Quasiconformal Mappings

1,2,*  and 1
1 Department of Mathematics, Technion, Technion City, Haifa 32000, Israel 2 Department of Mathematics and Computer Science, The Open University of Israel, 1 University Rd., Raanana 43107, Israel
* Author to whom correspondence should be addressed.
Received: 9 April 2012 / Revised: 31 May 2012 / Accepted: 11 June 2012 / Published: 4 July 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
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Abstract

We investigate the interplay between the existence of fat triangulations, P L approximations of Lipschitz–Killing curvatures and the existence of quasiconformal mappings. In particular we prove that if there exists a quasiconformal mapping between two P L or smooth n-manifolds, then their Lipschitz–Killing curvatures are bilipschitz equivalent. An extension to the case of almost Riemannian manifolds, of a previous existence result of quasimeromorphic mappings on manifolds due to the first author is also given.
Keywords: fat triangulation; Lipschitz–Killing curvatures; quasimeromorphic mapping fat triangulation; Lipschitz–Killing curvatures; quasimeromorphic mapping
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Saucan, E.; Katchalski, M. Fat Triangulations, Curvature and Quasiconformal Mappings. Axioms 2012, 1, 99-110.

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