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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the local structure of rank-one convex hulls

Author: László Székelyhidi Jr.
Journal: Proc. Amer. Math. Soc. 134 (2006), 1963-1972
MSC (2000): Primary 26B25
Published electronically: December 16, 2005
MathSciNet review: 2215765
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Abstract: In this note we prove that if $ K$ is a compact set of $ m\times n$ matrices containing an isolated point $ X$ with no rank-one connection into the convex hull of $ K\setminus\{X\}$, then the rank-one convex hull separates as

$\displaystyle K^{rc}=\bigl(K\setminus\{X\}\bigr)^{rc}\cup\{X\}. $

This is an extension of a result of P. Pedregal, which holds for $ 2\times 2$ matrices.

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Additional Information

László Székelyhidi Jr.
Affiliation: Departement Mathematik, ETH Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland

PII: S 0002-9939(05)08299-7
Received by editor(s): February 2, 2005
Published electronically: December 16, 2005
Additional Notes: The author thanks Bernd Kirchheim for pointing out this problem and for valuable discussions regarding rank-one convexity.
Communicated by: David Preiss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.