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

Reference:

Kreiner, C. F. and Zimmer, J., 2006. Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices. Esaim-Control Optimisation and Calculus of Variations, 12 (2), pp. 253-270.

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Official URL:

http://dx.doi.org/10.1051/cocv:2005036

Abstract

Continuing earlier work by Szekelyhidi, 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 R-2x2 is very rich; in particular, their collection is open as a subset of (R-2x2)(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.

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