An analogue of Koebe's theorem is proved for mappings obeying inverse moduli inequalities in metric spaces, with corollaries in Sobolev and Orlicz-Sobolev classes on surfaces and manifolds.
Volkov: On the Boundary Behavior of Mappings in the Class W^ 1,1 _ loc on Riemann Surfaces
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Proves prime-end boundary extensions for open discrete unclosed mappings in Orlicz-Sobolev classes, extending Carathéodory's theorem.
citing papers explorer
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An analogue of Koebe's theorem in metric spaces
An analogue of Koebe's theorem is proved for mappings obeying inverse moduli inequalities in metric spaces, with corollaries in Sobolev and Orlicz-Sobolev classes on surfaces and manifolds.
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On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes
Proves prime-end boundary extensions for open discrete unclosed mappings in Orlicz-Sobolev classes, extending Carathéodory's theorem.