| Issue |
ESAIM: COCV
Volume 12, Number 2, April 2006
|
|
|---|---|---|
| Page(s) | 253 - 270 | |
| DOI | https://doi.org/10.1051/cocv:2005036 | |
| Published online | 22 March 2006 | |
Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
1
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; zimmer@maths.bath.ac.uk
Received:
14
October
2004
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
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