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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2018: 2.316

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Mathematical Citation Quotient (MCQ) 2018: 1.44

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Volume 2, Issue 3


Chord-arc constants for submanifolds of arbitrary codimension

Simon Blatt
Published Online: 2009-04-28 | DOI: https://doi.org/10.1515/ACV.2009.011


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.

Keywords.: Submanifolds; chord-arc constant; BMO norm

About the article

Received: 2008-10-29

Published Online: 2009-04-28

Published in Print: 2009-07-01

Citation Information: Advances in Calculus of Variations, Volume 2, Issue 3, Pages 271–309, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/ACV.2009.011.

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