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Journal of Convex Analysis 21 (2014), No. 1, 253--260
Copyright Heldermann Verlag 2014

Right Convexity

Tudor Zamfirescu
Institute of Mathematics, Roumanian Academy of Sciences, P.O.B. 1-764, Bucharest 014700, Roumania

A convex set is F-convex if every pair of points in the set lie in a right triangle included in the set. We characterize F-convex sets, find some classes of F-convex sets, investigate F-convexity for cones and cylinders, and find out that most convex bodies are F-convex. On our way, we also describe the curvature at the endpoints of diameters of most convex bodies.

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