Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 175-178

A DISTANCE ESTIMATE ON THE BOUNDARY OF A CONFORMAL DEFORMATION OF THE UNIT BALL SATISFYING A HARNACK INEQUALITY AND THE GEHRING-HAYMAN PROPERTY

Timo Tossavainen

University of Eastern Finland, School of Applied Educational Science and Teacher Education
P.O. Box 86, FI-57101 Savonlinna, Finland; timo.tossavainen 'at' uef.fi

Abstract. We establish some bounds for the natural distance function on the boundary of such a conformal deformation of the unit ball Bⁿ, n \ge 2, that satisfies a Harnack inequality and the condition of the Gehring-Hayman theorem. The construction is useful especially for those points for which the radial limit exists.

2000 Mathematics Subject Classification: Primary 30C65.

Key words: Conformal deformation, conformal metric, Harnack inequality, Gehring-Hayman theorem.

Reference to this article: T. Tossavainen: A distance estimate on the boundary of a conformal deformation of the unit ball satisfying a Harnack inequality and the Gehring-Hayman property. Ann. Acad. Sci. Fenn. Math. 35 (2010), 175-178.

Full document as PDF file

doi:10.5186/aasfm.2010.3509