| Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积 |
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| 引用本文： | 赵霞,王卫东.Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积[J].数学学报,1936,63(4):409-416. |
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| 作者姓名： | 赵霞 王卫东 |
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| 作者单位： | 三峡大学理学院数学系 宜昌 443002 |
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| 基金项目： | 国家自然科学基金资助项目（11371224）；三峡大学硕士学位论文培优基金（2019SSPY144） |
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| 摘 要： | 2006年，Schuster提出了径向Blaschke-Minkowski同态的概念.随后，汪卫等人将其推广到Lp径向Blaschke-Minkowski同态.本文结合Lp对偶几何表面积，建立了Lp径向Blaschke-Minkowski同态的若干不等式，包括Brunn-Minkowski型不等式和单调不等式.并给出了Lp径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.
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Lp Dual Geominimal Surface Areas of Lp Radial Blaschke-Minkowski Homomorphisms |
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| Xia ZHAO,Wei Dong WANG.Lp Dual Geominimal Surface Areas of Lp Radial Blaschke-Minkowski Homomorphisms[J].Acta Mathematica Sinica,1936,63(4):409-416. |
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| Authors: | Xia ZHAO Wei Dong WANG |
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| Institution: | Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China |
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| Abstract: | In 2006, Schuster introduced the concept of radial Blaschke-Minkowski homomorphisms. Afterwards, Wang et al. extended this notion to Lp radial Blaschke-Minkowski homomorphisms. In this paper, we establish some inequalities of Lp dual geominimal surface areas for Lp radial Blaschke-Minkowski homomorphisms, including the Brunn-Minkowski type and monotonic inequalities. And we give an affirmative form and a negative form of Busemann-Petty problem for Lp radial Blaschke-Minkowski homomorphisms. |
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| Keywords: | Lp radial Blaschke-Minkowski homomorphism Lp dual geominimal surface area Brunn-Minkowski inequality Busemann-Petty problem |
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