Elasticae and inradius
Elasticae and inradius
复制标题
弹力带和内半径
DOI：
10.1007/s00013-016-0999-7
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发表时间：
2016
影响因子：
0.6
通讯作者：
Othmane Mounjid
中科院分区：
文献类型：
--
作者：
A. Henrot;Othmane Mounjid
平面凸体边界凸曲线的弹性能定义为其中k（s）是边界的曲率。在本文中，我们感兴趣的极小化问题的约束半径的。在所有其他最小化问题，涉及这个弹性能量（周长，面积，直径，或外接圆半径的限制）的解决方案始终是磁盘，我们在这里证明，这个最小化问题的解决方案是不是磁盘，我们完全描述它的基本功能。
The elastic energy of a convex curve bounding a planar convex bodyis defined bywherek(s) is the curvature of the boundary. In this paper we are interested in the minimization problem ofwith a constraint on the inradius of. In contrast to all the other minimization problems involving this elastic energy (with a perimeter, area, diameter, or circumradius constraints) for which the solution is always the disk, we prove here that the solution of this minimization problem is not the disk and we completely characterize it in terms of elementary functions.