Chord-arc constants for submanifolds of arbitrary codimension

Abstract

In this article we show that for k-dimensional submanifolds of which go through infinity in a smooth way, smallness of the Gromov distortion and some Ahlfors regularity is equivalent to smallness of the BMO norm of the unit normal and globally δ-Reifenberg flatness with small δ. This generalizes a result due to Semmes for hypersurfaces to surfaces of arbitrary codimension.