R^{2}中非重叠凸集的可塑性
The plasticity of non-overlapping convex sets in R^{2}
摘要：
研究了平面上加权Fermat-Torricelli问题的一个推广，它是用权为正实数的“小”闭凸曲线代替凸多边形的顶点而得到的，并研究了它的广义逆问题.我们的解决方案的基础上的一阶变分公式的长度的线段连接的加权Fermat-Torricelli点与其投影到给定的闭凸曲线。我们发现的“塑性”的解决方案，不重叠的圆与可变半径。
英文摘要：
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.
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