平均Minkowski对称度与对偶平均Minkowski对称度

发布时间：2018-04-15 05:02

本文选题：凸体 + 平均Minkowski对称度　；参考：《苏州科技学院》2015年硕士论文

【摘要】：本论文参照Toth教授引进的平均Minkowski对称度,引进一类新的凸体仿射几何不变量—对偶平均Minkowski对称度,并研究了这类对称度的一些性质。平均Minkowski对称度能够提供凸体低维截口对称程度的数量信息,而对偶平均Minkowski对称度能够提供凸体低维投影对称程度的数量信息。本文得到的主要成果是:(1)给出了低维凸体对偶平均Minkowski对称度的最佳上下界,并给出了相应的极值体。(2)给出了支撑支架的几个等价定义,并研究了其相应的性质。(3)证明了对偶平均Minkowski对称度的次等差性、超次可加性。
[Abstract]:In this paper, we introduce a new class of affine geometric invariants of convex bodies, duality mean Minkowski symmetry, according to the average Minkowski symmetry introduced by Professor Toth, and study some properties of this kind of symmetry degree.The average Minkowski symmetry can provide quantitative information on the degree of low dimensional sectional symmetry of convex bodies, while the dual average Minkowski symmetry degree can provide quantitative information on the degree of low dimensional projection symmetry of convex bodies.The main results obtained in this paper are: (1) the optimal upper and lower bounds of the dual average Minkowski symmetry of low dimensional convex bodies are given, and the corresponding extremum.In this paper, we also study its corresponding property. 3) and prove the subdifference and super subadditivity of the dual average Minkowski symmetry degree.
【学位授予单位】：苏州科技学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O186.5

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