{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:17Z","timestamp":1760243717804,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2012,7,4]],"date-time":"2012-07-04T00:00:00Z","timestamp":1341360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We investigate the interplay between the existence of fat triangulations, P L approximations of Lipschitz\u2013Killing 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\u2013Killing 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.<\/jats:p>","DOI":"10.3390\/axioms1020099","type":"journal-article","created":{"date-parts":[[2012,7,4]],"date-time":"2012-07-04T23:52:03Z","timestamp":1341445923000},"page":"99-110","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fat Triangulations, Curvature and Quasiconformal Mappings"],"prefix":"10.3390","volume":"1","author":[{"given":"Emil","family":"Saucan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technion, Technion City, Haifa 32000, Israel"},{"name":"Department of Mathematics and Computer Science, The Open University of Israel, 1 University Rd., Raanana 43107, Israel"}]},{"given":"Meir","family":"Katchalski","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technion, Technion City, Haifa 32000, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2012,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.5186\/aasfm.1977.0317","article-title":"On the existence of automorphic quasimeromorphic mappings in Rn","volume":"3","author":"Martio","year":"1977","journal-title":"Ann. 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