Abstract

We study a generalization of the weighted Fermat-Torricelli 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 Fermat-Torricelli point with its projections onto given closed convex curves. We find the 'plasticity' solutions for non-overlapping circles with variable radius.

Author information

Contact details are reproduced from the original publication and may be historical.

Anastasios N. Zachos

Department of Mathematics, University of Patras, 26500 Rion, Greece

azachos@gmail.com

Keywords

  • Fermat-Torricelli problem
  • convex
  • curve
  • variation
  • inverse problem
  • plasticity of non-overlapping closed convex sets

Mathematics Subject Classification

51E10, 51N20, 51P05, 70E17, 70F15, 70G75, 93B27

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Suggested citation

A. N. Zachos. “The Plasticity of Non-Overlapping Convex Sets in ℝ^2.” Journal of Convex Analysis 26 (2019), No. 3, 773–784. https://doi.org/10.68381/jca26042

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press.