6533b862fe1ef96bd12c60cd
RESEARCH PRODUCT
Compactness of a conformal boundary of the Euclidean unit ball
Päivi Lammisubject
CombinatoricsUnit sphereCompact spaceLogarithmGeneral MathematicsMathematical analysisEuclidean geometryMetric (mathematics)Boundary (topology)Conformal mapMathematicsHarnack's inequalitydescription
We study conformal metrics d‰ on the Euclidean unit ball B n : We assume that either the density ‰ associated with the metric d‰ satisfies a logarithmic volume growth condition for small balls or that ‰ satisfies a Harnack inequality and a suitable sub-Euclidean volume growth condition. We prove that the ‰-boundary @‰ B n is homeomorphic to S ni1 if and only if @‰ B n is compact. In the planar case, the compactness of @‰ B 2 is further equivalent to local connectivity of the ‰-boundary together with the boundedness of (B 2 ;d‰):
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 | Annales Academiae Scientiarum Fennicae Mathematica |