关于ℝⁿ中超曲面的新加权几何不等式的说明

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society 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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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.