| 摘要: |
| 本文研究了相关齐次函数的仿射球定理.利用Hopf极大值原理，对任意给定的带凹性条件的初等对称曲率问题，获得了此类仿射球定理.特别地，这也给出了Deicke齐次函数定理的一个新证明. |
| 关键词: 仿射球定理 齐次函数 |
| DOI： |
| 分类号:O175.25 |
| 基金项目:Supported by the Science and Technology Research program of Chongqing Municipal Education Commission (KJ1705136). |
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| A PROPER AFFINE SPHERE THEOREM RELATED TO HOMOGENEOUS FUNCTIONS |
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ZHAO Lei-na1,2
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1.College of Mathematics and Statistics;2.College of Transportation, Chongqing Jiaotong University, Chongqing 400074, China
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| Abstract: |
| In this paper, we focus on the affine sphere theorem related to homogeneous function. Based on Hopf maximum principle, we obtain that the affine sphere theorem does hold for given elementary symmetric curvature problems under concavity conditions. In particular, it gives a new proof of Deicke's theorem on homogeneous functions. |
| Key words: affine sphere theorem homogeneous functions |
