A geometric approach to the topological disk theorem of Reifenberg

Guanghao Hong and Lihe Wang

Vol. 233 (2007), No. 2, 321–339

DOI: 10.2140/pjm.2007.233.321

Abstract

We offer a new approach to the classical topological disk theorem of Reifenberg in the codimension-1 case. Our proof, using -level sets of the smoothing of the characteristic function of the domain Ω as approximating surfaces of ∂Ω, is much simpler than Reifenberg’s original one (1960). We also extend the result to parabolic space.

Keywords

topological disk, Reifenberg flat, parabolic distance

Mathematical Subject Classification 2000

Primary: 49Q15, 28A15

Milestones

Received: 5 January 2007

Revised: 31 May 2007

Accepted: 18 June 2007

Published: 1 December 2007