TY - JOUR
T1 - Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
AU - Kreiner, C F
AU - Zimmer, J
N1 - ID number: ISI:000236197700004
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
UR - http://dx.doi.org/10.1051/cocv:2005036
UR - https://www.scopus.com/pages/publications/33645798341
U2 - 10.1051/cocv:2005036
DO - 10.1051/cocv:2005036
M3 - Article
SN - 1262-3377
VL - 12
SP - 253
EP - 270
JO - Esaim-Control Optimisation and Calculus of Variations
JF - Esaim-Control Optimisation and Calculus of Variations
IS - 2
ER -