Fat Triangulations, Curvature and Quasiconformal Mappings
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 Lip...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2012-07-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2075-1680/1/2/99 |
| _version_ | 1818976931635265536 |
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| author | Emil Saucan Meir Katchalski |
| author_facet | Emil Saucan Meir Katchalski |
| author_sort | Emil Saucan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T16:19:41Z |
| format | Article |
| id | doaj.art-4f37dc17950b4040a1e19362bcf718a7 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-20T16:19:41Z |
| publishDate | 2012-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4f37dc17950b4040a1e19362bcf718a72022-12-21T19:33:41ZengMDPI AGAxioms2075-16802012-07-01129911010.3390/axioms1020099Fat Triangulations, Curvature and Quasiconformal MappingsEmil SaucanMeir KatchalskiWe 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.http://www.mdpi.com/2075-1680/1/2/99fat triangulationLipschitz–Killing curvaturesquasimeromorphic mapping |
| spellingShingle | Emil Saucan Meir Katchalski Fat Triangulations, Curvature and Quasiconformal Mappings Axioms fat triangulation Lipschitz–Killing curvatures quasimeromorphic mapping |
| title | Fat Triangulations, Curvature and Quasiconformal Mappings |
| title_full | Fat Triangulations, Curvature and Quasiconformal Mappings |
| title_fullStr | Fat Triangulations, Curvature and Quasiconformal Mappings |
| title_full_unstemmed | Fat Triangulations, Curvature and Quasiconformal Mappings |
| title_short | Fat Triangulations, Curvature and Quasiconformal Mappings |
| title_sort | fat triangulations curvature and quasiconformal mappings |
| topic | fat triangulation Lipschitz–Killing curvatures quasimeromorphic mapping |
| url | http://www.mdpi.com/2075-1680/1/2/99 |
| work_keys_str_mv | AT emilsaucan fattriangulationscurvatureandquasiconformalmappings AT meirkatchalski fattriangulationscurvatureandquasiconformalmappings |