Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 83-93 (2007)

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Curvature and $q$-strict convexity

Leoni Dalla and Evangelia Samiou

Department of Mathematics, University of Athens Panepistimioupolis, GR-15784 Athens, Greece, e-mail:; University of Cyprus, Department of Mathematics and Statistics, P.O. Box 20537, 1678 Nicosia, Cyprus, e-mail:

Abstract: We relate $q$-strict convexity of compact convex sets $K\subset\R^d$ whose boundary $\partial K$ is a differentiable manifold of class $C^q$ to intrinsic curvature properties of $\partial K$. Furthermore we prove that the set of $q$-strictly convex sets is $F_\sigma$ of first Baire category.

Keywords: $q$-strict convexity, curvature

Classification (MSC2000): 52A20, 53A05

Full text of the article:

Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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