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

Article

Fat Triangulations, Curvature and Quasiconformal Mappings

Emil Saucan ^1,2,*  and Meir Katchalski 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; in revised form: 31 May 2012 / Accepted: 11 June 2012 / Published: 4 July 2012

(This article belongs to the Special Issue Axioms: Feature Papers)

Download PDF Full-Text [212 KB, uploaded 4 July 2012 10:22 CEST]

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

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