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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
69/2003

Rank-One Convex Hulls in $\Bbb R^{2\times 2}$

László Székelyhidi

Abstract

We study the rank-one convex hull of compact sets $K\subset\R^{2\times 2}$. We show that if $K$ contains no two matrices whose difference has rank one, and if $K$ contains no four matrices forming a $T_4$ configuration, then the rank-one convex hull $K^{rc}$ is equal to $K$. Furthermore, we give a simple numerical criterion for testing for $T_4$ configurations.

Received:
Jul 27, 2003
Published:
Jul 27, 2003
MSC Codes:
49J45, 52A30
Keywords:
rank-one convexity

Related publications

inJournal
2005 Repository Open Access
László Székelyhidi

Rank-one convex hulls in \(\mathbb{R}^{2\times2}\)

In: Calculus of variations and partial differential equations, 22 (2005) 3, pp. 253-281