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

Primary: 49Q15, 28A15

Authors