支持功能的最大值和最小值

IF 0.6 4区 数学 Q3 MATHEMATICS
Huhe HAN
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引用次数: 0

摘要

对于给定的连续函数$\gamma_{{}_{i}}: S^{n}\to \mathbb{R}_{+}$ ($i=1, 2$),可以自然地定义函数$\gamma_{{}_{\max}}$和$\gamma_{{}_{\min}}$。本文应用球面方法,首先证明了当$\gamma_{{}_1}$和$\gamma_{{}_2}$为凸积分时,与$\gamma_{{}_{\max}}$相关的Wulff形状是与$\gamma_{{}_1}$和$\gamma_{{}_2}$相关的Wulff形状并集的凸包。接下来,我们将展示与$\gamma_{{}_{\min}}$相关的Wulff形状是与$\gamma_{{}_1}$和$\gamma_{{}_2}$相关的Wulff形状的交集。并给出了它们的对偶Wulff形之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Maximum and minimum of support functions
For given continuous functions $\gamma_{{}_{i}}: S^{n}\to \mathbb{R}_{+}$ ($i=1, 2$), the functions $\gamma_{{}_{\max}}$ and $\gamma_{{}_{\min}}$ can be defined naturally. In this paper, by applying the spherical method, we first show that the Wulff shape associated to $\gamma_{{}_{\max}}$ is the convex hull of the union of Wulff shapes associated to $\gamma_{{}_1}$ and $\gamma_{{}_2}$, if $\gamma_{{}_1}$ and $\gamma_{{}_2}$ are convex integrands. Next, we show that the Wulff shape associated to $\gamma_{{}_{\min}}$ is the intersection of Wulff shapes associated to $\gamma_{{}_1}$ and $\gamma_{{}_2}$. Moreover, relationships between their dual Wulff shapes are given.
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The main purpose of Hokkaido Mathematical Journal is to promote research activities in pure and applied mathematics by publishing original research papers. Selection for publication is on the basis of reports from specialist referees commissioned by the editors.
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