Open discrete mappings with unbounded coefficient of quasi-conformality on Riemannian manifolds

D. P. Il'yutko   ; E. A. Sevost'yanov

Sbornik. Mathematics, Tome 207 (2016) no. 4, pp. 537-580

Résumé

The paper is concerned with problems at the intersection of the theory of spatial quasi-conformal mappings and the theory of Riemann surfaces. Theorems on the local behaviour of one class of open discrete mappings with unbounded coefficient of quasi-conformality, which map between arbitrary Riemannian manifolds, are obtained. Such mappings are also shown to extend to isolated points of the boundary of the domain. Some results on the local behaviour of Sobolev and Orlicz-Sobolev classes are obtained as an application. Bibliography: 52 titles.

Détail

Keywords: Riemannian manifold, modulus of families of paths and surfaces, mapping of bounded or finite distortion, local and global behaviour of mappings, Orlicz-Sobolev class.

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