### 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 |
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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

Zhang, K. (1997). On connected subsets of M

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