Non-compact lamination convex hulls

Jan Kolár

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Submission date: 13. Mar. 2001
Pages: 13
published in: Annales de l'Institut Henri Poincaré / C, 20 (2003) 3, p. 391-403 
DOI number (of the published article): 10.1016/S0294-1449(02)00007-0
Bibtex
MSC-Numbers: 26B25, 52A30
Keywords and phrases: lamination convex hull, bi-convexity, separate convexity

Abstract:
We give an example of a compact set K of symmetric two by two matrices such that its lamination convex hull is not compact, and similar examples for separate convexity in R³ and bi-convexity in R² x R. Furthermore we show that the operator, mapping a compact set onto the closure of its lamination convex hull, is not upper semi-continuous with respect to Hausdorff metric on the space of all compact sets K of diagonal 3 x 3 matrices.The paper is aviable online from Elsevier at

http://dx.doi.org/10.1016/S0294-1449(02)00007-0.