共形公设体积的三圆定理

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics Pub Date : 2024-05-11 DOI:10.1007/s40304-024-00394-6

Zihao Wang, Jie Zhou

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引用次数: 0

摘要

在本文中，我们为标量曲率在临界（缩放不变）规范下可积分的共形度量建立了三圈定理。作为应用，我们分析了孤立奇点附近这类度量的渐近行为，并用它来证明 Chern-Gauss-Bonnet 公式的残差项是整数。这种强刚性意味着关于 \(Q_g\) 曲率积分值的消失定理，可应用于保角度量的双利普希茨等价问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Three Circles Theorem for Volume of Conformal Metrics

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Three Circles Theorem for Volume of Conformal Metrics

In this paper, we establish three circles theorem for volume of conformal metrics whose scalar curvatures are integrable in a critical (scaling invariant) norm. As applications, we analyze the asymptotic behavior of such metrics near isolated singularities and use it to show the residual terms of the Chern–Gauss–Bonnet formula are integers. Such strong rigidity implies a vanishing theorem on the integral value of the \(Q_g\) curvature, with application to the bi-Lipschitz equivalence problem for conformal metrics.

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来源期刊

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.