Maximum length of steepest descent curves for quasi-convex functions
Maximum length of steepest descent curves for quasi-convex functions
复制标题
拟凸函数的最速下降曲线的最大长度
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
C. Pucci
中科院分区：
文献类型：
--
作者：
P. Manselli;C. Pucci
平面的、定向的、可校正的曲线，使得在几乎每个x中，法线界定包含在x之前的曲线部分的半平面。结果表明，在上述曲线族中，对于给定周长的凸包，存在长度最大的曲线，这些曲线都是其自身的演化曲线。证明了集Ω中的拟凸函数有最陡的下降线，其长度以Ω的直径为界。然后将这一结果推广到ℝn。
Plane, oriented, rectifiable curves, such that, in almost each x the normal line bounds a half-plane containing the part of the curve preceding x, are considered. It is shown that, in the family of curves as above, with convex hull of given perimeter, there exist curves of maximal length and these are evolutes of themselves. As a consequence, it is proved that quasi-convex functions in a set Ω have steepest descent lines with length bounded by the diameter of Ω. This result is then extended to ℝn.