Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T08:39:06.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Strict convexity of sets in analytic terms

Part of: General convexity

Published online by Cambridge University Press:  09 April 2009

Leoni Dalla  and
Telemachos Hatziafratis
Leoni Dalla
Affiliation:
The University of Athens, Department of Mathematics, Panepistemiopolis 15784, Athens, Greece, e-mail: [email protected], [email protected]. gr
Telemachos Hatziafratis
Affiliation:
The University of Athens, Department of Mathematics, Panepistemiopolis 15784, Athens, Greece, e-mail: [email protected], [email protected]. gr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compare the geometric concept of strict convexity of open subsets of Rn with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2N-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.

Keywords

strictly convex set2N-strictly convex setdefining functionexhaustion of a convex set.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 49 - 62
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Klee, V., ‘Some new results on smoothness and rotundity in normed linear spaces’, Math. Ann. 139 (1959), 51–63.CrossRefGoogle Scholar
[2]Range, R. M., Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics 108 (Springer, New York, 1986).CrossRefGoogle Scholar
[3]Zamfirescu, T., ‘Nearly all convex bodies are smooth and strictly convex’, Monatsh. Math. 103 (1987), 57–62.CrossRefGoogle Scholar
[4]Zamfiresu, T., ‘Baire categories in convexity’, Attl. Sem. Mat. Fis. Univ. Modena 39 (1991), 139–164.Google Scholar