On connected subsets of M2×2 without rank-one connections
1997 ◽
Vol 127
(1)
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pp. 207-216
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Keyword(s):
Rank One
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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.