星体的Bonnesen-型不等式

摘要/Abstract

摘要：

受Lutwak与Petty工作[25-26, 37]的启发，该文构造了关于给定凸体$K$的一类新型星体${\cal G}K$，建立了关于${\cal G}K$的等周不等式，并由此给出关于凸体K的逆Bonnesen-型等周不等式.

关键词: 等周不等式, Bonnesen-型等周不等式, 微分仿射等周不等式, 星体

Abstract:

Motivated by works of Lutwak and Petty[25-26, 37], a new star body ${\cal G}K$ associated with a given convex body $K$ is constructed. The isoperimetric inequality for ${\cal G}K$ and the reverse Bonnesen-style inequalities for K are established.

Key words: isoperimetric inequality, Bonnesen-style isoperimetric Inequality, Differential affine isoperimetric inequality, Star body

中图分类号:

O186.5

张增乐. 星体的Bonnesen-型不等式[J]. 数学物理学报, 2021, 41(5): 1249-1262.

Zengle Zhang. Bonnesen-Style Inequalities for Star Bodies[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1249-1262.

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