Date: 12 May 2004

Rank-one convex hulls in \(\mathbb{R}^{2\times2}\)

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We study the rank-one convex hull of compact sets \(K\subset\mathbb{R}^{2\times2}\) . We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a T 4 configuration, then the rank-one convex hull K rc is equal to K. Furthermore, we give a simple numerical criterion for testing for T 4 configurations.

Received: 20 August 2003, Accepted: 3 March 2004, Published online: 12 May 2004

Mathematics Subject Classification (2000):

49J45, 52A30

An erratum to this article can be found at