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

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An Erratum to this article was published on 09 January 2007

Abstract.

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.

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Authors and Affiliations

  1. Institute for Advanced Study,, Einstein Drive,, NJ 08540,, Princeton, USA

    László Székelyhidi Jr.

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  1. László Székelyhidi Jr.
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Correspondence to László Székelyhidi Jr..

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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 http://dx.doi.org/10.1007/s00526-006-0053-x

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Székelyhidi, L. Rank-one convex hulls in \(\mathbb{R}^{2\times2}\) . Calc. Var. 22, 253–281 (2005). https://doi.org/10.1007/s00526-004-0272-y

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