偏对称2张量场协变导数散度下界的反例

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-03-21 DOI:10.1007/s10455-023-09896-y

Stefano Borghini, Lorenzo Mazzieri

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引用次数: 4

摘要

在Hwang和Yun（Ann Glob Anal Geom 62（3）:507–5322022）中，提出了对斜对称2-张量的估计。不久之后，这一估计被用来声称有强大的分类结果：最值得注意的是，它被用来提出具有正标量曲率的真空静态时空的黑洞唯一性定理的证明（Xu和Ye在Invent Math 33（2）:64，2022），并与贝塞尔猜想（Yun和Hwang在三维流形上的临界点方程和贝塞尔猜想中）有关。在本说明中，我们指出了Hwang和Yun（Ann Glob Anal Geom 62（3）:507–5322022）中提出的论点中的一个问题，并为该估计提供了一个反例。

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Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

In Hwang and Yun (Ann Glob Anal Geom 62(3):507–532, 2022), an estimate for skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: Most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes with positive scalar curvature (Xu and Ye in Invent Math 33(2):64, 2022) and in connection with the Besse conjecture (Yun and Hwang in Critical point equation on three-dimensional manifolds and the Besse conjecture). In the present note, we point out an issue in the argument proposed in Hwang and Yun (Ann Glob Anal Geom 62(3):507–532, 2022) and we provide a counterexample to the estimate.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.