*Published Paper*

**Inserted:** 14 nov 2002

**Last Updated:** 3 may 2011

**Journal:** C. R. Math. Acad. Sci. Paris

**Volume:** 337

**Number:** 4

**Pages:** 233-238

**Year:** 2003

**Abstract:**

We give a short, self-contained argument showing that, for compact connected sets in $M^{2\times 2}$ 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.

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