Annales Academię Scientiarum Fennicę

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 **B**^{n}, *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

Copyright © 2010 by Academia Scientiarum Fennica