On the locally branched Euclidean metric gauge

On the locally branched Euclidean metric gauge

Juha Heinonen and Dennis Sullivan

Source: Duke Math. J. Volume 114, Number 1 (2002), 15-41.

Abstract

A metric gauge on a set is a maximal collection of metrics on the set such that the identity map between any two metrics from the collection is locally bi-Lipschitz. We characterize metric gauges that are locally branched Euclidean and discuss an obstruction to removing the branching. Our characterization is a mixture of analysis, geometry, and topology with an argument of Yu. Reshetnyak to produce the branched coordinates for the gauge.

Primary Subjects: 30C65

Secondary Subjects: 58A99

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1087575355
Mathematical Reviews number (MathSciNet): MR1 915 034
Digital Object Identifier: doi:10.1215/S0012-7094-02-11412-4
Zentralblatt MATH identifier: 1019.58002

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