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

Kewei Zhang

On connected subsets of M^2×2 without rank-one connections

Kewei Zhang

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that connected subsets of M^2×2 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.

Original language	English
Pages (from-to)	207-216
Number of pages	10
Journal	Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume	127
Issue number	1
Publication status	Published - 1997

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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.",

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AB - 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.

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JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

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On connected subsets of M^2×2 without rank-one connections

Abstract

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