Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26B25

Retrieve articles in all journals with MSC (2000): 26B25


Additional Information

László Székelyhidi Jr.
Affiliation: Departement Mathematik, ETH Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland
Email: szekelyh@math.ethz.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08299-7
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.