Quasihyperbolic boundary condition: Compactness of the inner boundary
Lammi, P. (2011). Quasihyperbolic boundary condition: Compactness of the inner boundary. Illinois Journal of Mathematics, 55 (3), 1221-1233. doi:10.1215/ijm/1371474552
Published inIllinois Journal of Mathematics
© 2013 University of Illinois
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.
PublisherUniversity of Illinois
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