Conformal repellors with dimension one are Jordan curves

R. Daniel Mauldin and Mariusz Urbanski

Vol. 166 (1994), No. 1, 85–97

DOI: 10.2140/pjm.1994.166.85

Abstract

We show that a conformal repellor in ℝ^m whose Hausdorff and topological dimensions are equal to 1 is a Jordan curve. Moreover, its 1-dimensional Hausdorff measure is finite and it has a tangent at every point.

Mathematical Subject Classification 2000

Primary: 58F12

Secondary: 28C99

Milestones

Received: 27 October 1992

Revised: 3 November 1993

Accepted: 15 November 1993

Published: 1 November 1994