### 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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### Cite this

^{2×2}without rank-one connections.

*Proceedings of the Royal Society of Edinburgh, Section A: Mathematics*,

*127*(1), 207-216.

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^{2×2}without rank-one connections',

*Proceedings of the Royal Society of Edinburgh, Section A: Mathematics*, vol. 127, no. 1, pp. 207-216.

**On connected subsets of M ^{2×2} without rank-one connections.** / Zhang, Kewei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On connected subsets of M2×2 without rank-one connections

AU - Zhang, Kewei

PY - 1997

Y1 - 1997

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=21444441022&partnerID=8YFLogxK

M3 - Article

VL - 127

SP - 207

EP - 216

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

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

SN - 0308-2105

IS - 1

ER -

^{2×2}without rank-one connections. Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. 1997;127(1):207-216.