Chord-Arc Constants for Submanifolds of Arbitrary

Blatt, Simon

doi:10.1515/ACV.2009.011, /July/2009

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Chord-Arc Constants for Submanifolds of Arbitrary

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Blatt, Simon
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Blatt, S. (2009). Chord-Arc Constants for Submanifolds of Arbitrary. Advances in Calculus of Variations, 2(3), 271-309. doi:10.1515/ACV.2009.011, /July/2009.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-459C-9

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.