Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices

C F Kreiner, J Zimmer

Research output: Contribution to journalArticle

3 Citations (Scopus)
129 Downloads (Pure)

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 languageEnglish
Pages (from-to)253-270
Number of pages18
JournalEsaim-Control Optimisation and Calculus of Variations
Volume12
Issue number2
Early online date22 Mar 2006
DOIs
Publication statusPublished - 2006

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