Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 83-93 (2007)
Curvature and $q$-strict convexity
Leoni Dalla and Evangelia SamiouDepartment of Mathematics, University of Athens Panepistimioupolis, GR-15784 Athens, Greece, e-mail: firstname.lastname@example.org; University of Cyprus, Department of Mathematics and Statistics, P.O. Box 20537, 1678 Nicosia, Cyprus, e-mail: email@example.com
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
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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.