Rn$\mathbb {R}^n$ 中超曲面的加权亚历山德罗夫-芬切尔式不等式

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-24 DOI:10.1112/blms.13089

Jie Wu

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摘要

在本文中，我们证明了欧几里得空间中的下列几何不等式，它们是加权亚历山德罗夫-芬切尔式不等式，条件是星形和-凸超曲面。当且仅当是坐标球面时，等式成立。作为应用，通过在上述不等式中留空，我们可以得到星形和-凸超曲面曲率积分的外半径下限。

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Weighted Alexandrov–Fenchel type inequalities for hypersurfaces in R n $\mathbb {R}^n$

In this paper, we prove the following geometric inequalities in the Euclidean space $R^{n} (n ⩾ 3)$ , which are weighted Alexandrov–Fenchel type inequalities,