A geometric approach to the topological disk theorem of Reifenberg

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.