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On connected subsets of M2×2 without rank-one connections

Published online by Cambridge University Press:  14 November 2011

Kewei Zhang
Kewei Zhang
Affiliation:
School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, NSW 2109, Australia* e-mail: [email protected]
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Abstract

We prove that connected subsets of M2×2 without rank-one connections are Lipschitz graphs of mappings from subsets of a fixed two-dimensional subspace to its orthogonal complement. Under a weaker condition that the set does not have rank-one connections locally, we are able to establish some global results on the set. We also establish some results on Lipschitz extensions of the functions thus obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 207 - 216
Copyright
Copyright © Royal Society of Edinburgh 1997

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