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

Kewei Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)207-216
Number of pages10
JournalProceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume127
Issue number1
Publication statusPublished - 1997

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