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On connected subsets of M2×2 without rank-one connections
Published online by Cambridge University Press: 14 November 2011
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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