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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
98/2002

Polyconvexity equals rank-one convexity for connected isotropic sets in $M^{2\times 2}$

Sergio Conti, Camillo De Lellis, Stefan Müller and Mario Romeo

Abstract

We give a short, self-contained argument showing that, for compact connected sets in $M^{2\times2}$ which are invariant under the left and right action of SO(2), polyconvexity is equivalent to rank-one convexity (and even to lamination convexity). As a corollary, the same holds for O(2)-invariant compact sets. These results were first proved by Cardaliaguet and Tahraoui. We also give an example showing that the assumption of connectedness is necessary in the SO(2) case.

Received:
Nov 6, 2002
Published:
Nov 6, 2002

Related publications

inJournal
2003 Repository Open Access
Sergio Conti, Camillo De Lellis, Stefan Müller and Mario Romeo

Polyconvexity equals rank-one convexity for connected isotropic sets in M 2*2

In: Comptes rendus mathematique, 337 (2003) 4, pp. 233-238