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



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 T4 configuration, then the rank-one convex hull Krc is equal to K. Furthermore, we give a simple numerical criterion for testing for T4 configurations.


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© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institute for Advanced Study,PrincetonUSA

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