Steiner对称化后对偶混合体积部分性质
Partial Properties of Dual Mixed Volumes by Steiner Symmertrization
DOI: 10.12677/PM.2023.137201, PDF,    国家自然科学基金支持
作者: 李朝衡：重庆工商大学，数学与统计学院，重庆
关键词: 径向加法；对偶混合体积；Steiner对称化；对偶Minkowski不等式；Radial Addition； Dual Mixed Volumes； Steiner Symmetrization； Dual Minkowski Inequality
摘要: 在本文中，我们探讨对偶混合体的性质，考虑在星体的径向加法下，星体经过Steiner对称化后做加法与先加后做Steiner对称化两者之间的包含关系，继而利用包含性来得到星体经过Steiner对称化后相应的对偶混合体积性质，最后利用高斯球逼近定理构建单调序列来证明特殊星体的对偶Minkowski不等式。
Abstract: In this paper, we study the property of the dual mixed volumes, and consider the inclusive relation-ships between the radial addition of the star bodies after Steiner symmetrization and the symmetrization after doing the addition first. Then we use the inclusion to gain the trend of the dual mixed volumes after symmetrization. Finally, the Gaussian sphere approximation theorem is used to construct monotone sequences to prove the dual Minkowski inequality for special star bodies.
文章引用：李朝衡. Steiner对称化后对偶混合体积部分性质[J]. 理论数学, 2023, 13(7): 1953-1958. https://doi.org/10.12677/PM.2023.137201

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