Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
Max Planck Institute for
Mathematics in the Sciences, Inselstr. 22, 04 103 Leipzig, Germany.
2 University of Bath, Department of Mathematical Sciences, Claverton Down, Bath BA2 7AY, UK; email@example.com
Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called T4-configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of T4-configurations in is very rich; in particular, their collection is open as a subset of . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm to detect T4-configurations.
Mathematics Subject Classification: 49J45 / 52A30
Key words: Rank-one convexity / T4-configurations.
© EDP Sciences, SMAI, 2006