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Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 2 / April 2006
- Published online by Cambridge University Press:
- 22 March 2006, pp. 253-270
- Print publication:
- April 2006
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- Article
- Export citation
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Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called T 4-configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of T 4-configurations in $\mathbb{R}^{2\times 2}$
is very rich; in particular, their collection is open as a subset of $(\mathbb{R}^{2\times2})^{4}$ 
. Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm to detect T 4-configurations.
