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.
- Acta Math
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Mappings satisfying inverse Poletskii-type modulus inequalities are equicontinuous w.r.t. prime ends of domains provided the majorant is integrable.
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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 equicontinuity of mappings with inverse moduli inequalities by prime ends of variable domains
Mappings satisfying inverse Poletskii-type modulus inequalities are equicontinuous w.r.t. prime ends of domains provided the majorant is integrable.