Quasiminimal surfaces of codimension 1 and John domains

Guy David and Stephen Semmes

Vol. 183 (1998), No. 2, 213–277

DOI: 10.2140/pjm.1998.183.213

Abstract

We study codimension 1 quasiminimizing surfaces in ℝⁿ, and establish uniform rectifiability and other geometric properties of these surfaces. For instance, their complementary components must be John domains. In fact we give a complete characterization of quasiminimizers. As an application we show that sets which are not too large and which separate points in a definite way must have a large uniformly rectifiable piece. In this way we use area quasiminimizers to solve a problem in geometric measure theory.

Milestones

Received: 30 October 1996

Published: 1 April 1998