Volume 24, Number 4, October–December 2018
|Page(s)||1503 - 1510|
|Published online||11 July 2018|
Upper semicontinuity of the lamination hull★
School of Mathematics and Statistics, University of New South Wales,
NSW 2052, Australia
2 Department of Mathematics, University of Illinois, Urbana IL 61801, USA
Corresponding author: firstname.lastname@example.org
Received in final form: 18 March 2017
Accepted: 21 April 2017
Let K ⊆ ℝ2×2 be a compact set, let Krc be its rank-one convex hull, and let L (K) be its lamination convex hull. It is shown that the mapping K ↦ L̅(K̅) is not upper semicontinuous on the diagonal matrices in ℝ2×2, which was a problem left by Kolář. This is followed by an example of a 5-point set of 2 × 2 symmetric matrices with non-compact lamination hull. Finally, another 5-point set K is constructed, which has L (K) connected, compact and strictly smaller than Krc.
Mathematics Subject Classification: 49J45 / 52A30
Key words: Lamination convexity / rank-one convexity
© EDP Sciences, SMAI 2018
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