Elsevier

Advances in Mathematics

Volume 85, Issue 2, February 1991, Pages 198-223
Advances in Mathematics

Chord-arc surfaces with small constant, I

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Abstract

We introduce a notion for hypersurfaces in Rd + 1 that is analogous to the chord-arc condition with small constant for curves in the plane. We give various equivalent operator-theoretic, function-theoretic, and geometrical characterizations of these surfaces. We not know any nice potential-theoretic characterizations. In a companion paper we address the issue of finding good parameterizations for these surfaces.

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The author is partially supported by the NSF and the Sloan Foundation.