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.
|Number of pages||18|
|Journal||Esaim-Control Optimisation and Calculus of Variations|
|Early online date||22 Mar 2006|
|Publication status||Published - 2006|
Kreiner, C. F., & 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), 253-270. https://doi.org/10.1051/cocv:2005036