
Journal of Convex Analysis 26 (2019), No. 3, 773784 Copyright Heldermann Verlag 2019 The Plasticity of NonOverlapping Convex Sets in R^{2} Anastasios N. Zachos Department of Mathematics, University of Patras, 26500 Rion, Greece azachos@gmail.com We study a generalization of the weighted FermatTorricelli problem in the plane, which is derived by replacing vertices of a convex polygon by 'small' closed convex curves with weights being positive real numbers on the curves, we also study its generalized inverse problem. Our solution of the problems is based on the first variation formula of the length of line segments that connect the weighted FermatTorricelli point with its projections onto given closed convex curves. We find the Keywords: FermatTorricelli problem, convex, curve, variation, inverse problem, plasticity of nonoverlapping closed convex sets. MSC: 51E10, 51N20, 51P05, 70E17, 70F15, 70G75, 93B27. [ Fulltextpdf (181 KB)] for subscribers only. 