### 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.

Original language | English |
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Pages (from-to) | 253-270 |

Number of pages | 18 |

Journal | Esaim-Control Optimisation and Calculus of Variations |

Volume | 12 |

Issue number | 2 |

Early online date | 22 Mar 2006 |

DOIs | |

Publication status | Published - 2006 |

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## Cite this

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