Illinois Journal of Mathematics

Quasihyperbolic boundary condition: Compactness of the inner boundary

Päivi Lammi

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Abstract

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

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

Dates
First available in Project Euclid: 17 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1371474552

Digital Object Identifier
doi:10.1215/ijm/1371474552

Mathematical Reviews number (MathSciNet)
MR3254021

Zentralblatt MATH identifier
1296.30035

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

Citation

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


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