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Licensed Unlicensed Requires Authentication Published by De Gruyter October 31, 2013

Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices

Sebastian Heinz

Abstract

Let K be a given compact set of real 2×2 matrices that is isotropic, meaning invariant under the left and right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides with the lamination convex hull of order 2. In particular, there is no difference between quasiconvexity, rank-one convexity and lamination convexity for K. This is a generalization of a known result for connected sets.

MSC: 26B25; 52A30

Funding source: DFG

Award Identifier / Grant number: FOR 797 under Mie 459/5-2

The author would like to acknowledge the very helpful discussions with Martin Kružík.

Received: 2012-5-16
Revised: 2013-6-21
Accepted: 2013-10-10
Published Online: 2013-10-31
Published in Print: 2015-1-1

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