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.
Springer-Verlag, Berlin
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Proves that open discrete mappings satisfying inverse Poletsky inequality with integrable majorant admit continuous boundary extensions when domain boundaries satisfy finite connectivity and non-density conditions.
Mappings satisfying inverse Poletskii-type modulus inequalities are equicontinuous w.r.t. prime ends of domains provided the majorant is integrable.
Equicontinuity of families of open discrete unclosed mappings satisfying inverse Poletsky inequalities is established via prime ends, yielding a result for Orlicz-Sobolev classes.
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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Carath\'eodory boundary extensions for generalized quasiregular mappings
Proves that open discrete mappings satisfying inverse Poletsky inequality with integrable majorant admit continuous boundary extensions when domain boundaries satisfy finite connectivity and non-density conditions.
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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.
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On Caratheodory theorem for open discrete unclosed mappings
Equicontinuity of families of open discrete unclosed mappings satisfying inverse Poletsky inequalities is established via prime ends, yielding a result for Orlicz-Sobolev classes.