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Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices

Carl-Friedrich KreinerJohannes Zimmer — 2006

ESAIM: Control, Optimisation and Calculus of Variations

Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called -configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of -configurations in 2 × 2 is very rich; in particular, their collection is open as a subset of ( 2 × 2 ) 4 . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm...

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