Illinois Journal of Mathematics

Quasihyperbolic boundary condition: Compactness of the inner boundary

Päivi Lammi

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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.

Article information

Illinois J. Math., Volume 55, Number 3 (2011), 1221-1233.

First available in Project Euclid: 17 June 2013

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Zentralblatt MATH identifier

Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations


Lammi, Päivi. Quasihyperbolic boundary condition: Compactness of the inner boundary. Illinois J. Math. 55 (2011), no. 3, 1221--1233. doi:10.1215/ijm/1371474552.

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