6533b870fe1ef96bd12cf400

RESEARCH PRODUCT

Quasihyperbolic boundary condition: Compactness of the inner boundary

Päivi Lammi

subject

Gromov boundaryquasihyperbolic metricMathematics::Complex VariablesGeneral Mathematicsgrowth conditionMathematical analysisBoundary (topology)Mixed boundary conditionGromov-reuna30C65Gromov boundaryMetric spaceCompact spaceGromov hyperbolicityGromov-hyperbolisuusMetric (mathematics)Neumann boundary conditionMathematics::Metric Geometrykasvuehtokvasihyperbolinen metriikkaBoundary value problemMathematics

description

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. peerReviewed

yearjournalcountryeditionlanguage
2011-01-01Illinois Journal of Mathematics
https://doi.org/10.1215/ijm/1371474552