Search results for "Gromov hyperbolicity"

showing 2 items of 2 documents

Quasihyperbolic boundary condition: Compactness of the inner boundary

2011

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

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 problemMathematicsIllinois Journal of Mathematics
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Gromov hyperbolicity and quasihyperbolic geodesics

2014

We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition. peerReviewed

Gromov hyperbolicityMathematics::Complex Variablesquasihyperbolic metricMathematics::Metric GeometryGehring-Hayman inequality
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