Vol. 233, No. 2, 2007

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ISSN: 0030-8730
A geometric approach to the topological disk theorem of Reifenberg

Guanghao Hong and Lihe Wang

Vol. 233 (2007), No. 2, 321–339
Abstract

We offer a new approach to the classical topological disk theorem of Reifenberg in the codimension-1 case. Our proof, using 1
2-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
Authors
Guanghao Hong
East Campus, Mailbox 1924
Xi’an Jiaotong University
Xi’an 710049
Shaanxi Province
China
Lihe Wang
Department of Mathematics
14 MacLean Hall
University of Iowa
Iowa City, IA 52242-1419
United States
www.math.uiowa.edu/~lwang