Kangaslampi R. Uniformly quasiregular mappings on elliptic Riemannian manifolds. - Helsinki, 2008. - 69 p. - (Annales Academiae Scientiarum Fennicae. Mathematica. Dissertationes; N 151). - ISBN 951-41-0989-9  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

1 Introduction .................................................. 7 1.1 History of the research on quasiregular mappings .......... 7 1.2 Overview of this thesis ................................... 8 2 Preliminary results ........................................... 9 2.1 Normal coordinates ........................................ 9 2.2 Geodetically convex neighbourhood ........................ 10 2.3 Locally bilipschitz-continuous coordinate charts ......... 14 3 Definitions and properties of quasiregular mappings .......... 17 3.1 Quasiregular mappings .................................... 17 3.2 Branch set ............................................... 18 3.3 Uniformly quasiregular mappings .......................... 19 3.4 Lattes-type mappings ..................................... 21 3.5 Normal family ............................................ 21 4 Dynamics of uniformly quasiregular mappings .................. 23 4.1 Local representations .................................... 23 4.2 Julia sets ............................................... 26 5 Rescaling principle .......................................... 32 5.1 Criteria for normality ................................... 32 5.2 Rescaling principle on manifolds ......................... 36 5.3 Manifolds supporting uqr-mappings are elliptic ........... 45 6 Elliptic 3-manifolds ......................................... 47 6.1 Representation by a polyhedron ........................... 47 6.2 3-dimensional model geometries ........................... 47 7 Uniformly quasiregular mappings on elliptic 3-manifolds ...... 51 7.1 Spherical space forms .................................... 51 7.2 Euclidean space forms .................................... 51 7.2.1 Manifolds with tetragonal basis .................... 52 7.2.2 Manifolds with hexagonal basis ..................... 56 7.3 Manifolds covered by S2×R ................................ 61 7.3.1 Sphere bundle S2×S ................................. 61 7.3.2 Connected sum P3#P3 ................................ 64 References ..................................................... 68