三角形与任意单点生成凸包的Minkowski非对称度（英文）

Minkowski measure of asymmetry for the convex hull of a triangle and a point

作为最重要的几何仿射不变量,凸体的非对称度近年来重新引起了众多研究者的关注与研究。文中讨论了平面上一个三角形与任意单点生成凸包的Minkowski非对称度,给出了此类凸体Minkowski非对称度的精确计算公式,并揭示了这类凸体Minkowski非对称度的某些有趣性质。

As one of the most important geometric affine invariants, the measure of asymmetry for convex bodies has recently regained more and more attention of researchers. This paper discussed the Minkowski measure of asymmetry for the convex hull of a triangle and a point in hope to find some particular properties of the Minkowski measures. A precise expression of the Minkowski measure for such convex bodies was given. It shows that the Minkowski measure does have some interesting properties in the case we studied.