关于ℝⁿ中超曲面的新加权几何不等式的说明

Pub Date : 2024-04-10 DOI:10.1090/proc/16875

Jie Wu

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引用次数: 0

摘要

在本注释中，我们证明了一系列尖锐的权重不等式，它们涉及 R n \mathbb {R}^n 中封闭超曲面的加权 k k -th 平均曲率积分和两个不同的质点积分。这个不等式概括了 Wei 和 Zhou [Bull. Lond. Math. Soc. 55 (2023), pp.267 (2014), pp.Contemp.Math.17 (2015), p. 1550014].这里我们提出一个不依赖邝淼结果的证明。

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A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ

In this note, we prove a family of sharp weighed inequalities which involve weighted k k -th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in R n \mathbb {R}^n . This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao’s results.

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