Three Circles Theorem for Volume of Conformal Metrics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-11 DOI:10.1007/s40304-024-00394-6

Zihao Wang, Jie Zhou

引用次数: 0

Abstract

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.

Abstract Image

查看原文本刊更多论文

共形公设体积的三圆定理

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.