Volume 12, Number 2, April 2006
|Page(s)||253 - 270|
|Published online||22 March 2006|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.