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Quasihyperbolic boundary condition: compactness of the inner boundary. (English) Zbl 1296.30035
Summary: We prove that if a metric space satisfies a suitable growth condition in the quasihyperbolic metric and the Gehring-Hayman theorem in the original metric, then the inner boundary of the space is homeomorphic to the Gromov boundary. Thus, the inner boundary is compact.

MSC:
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
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Full Text: Euclid
References:
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