Gravitational instantons with quadratic volume growth

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-03-30 DOI:10.1112/jlms.12886

Gao Chen, Jeff Viaclovsky

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引用次数: 0

Abstract

There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type $ALG$ and ${ALG}^{*}$ . Gravitational instantons of type $ALG$ were previously classified by Chen–Chen. In this paper, we prove a classification theorem for ${ALG}^{*}$ gravitational instantons. We determine the topology and prove existence of “uniform” coordinates at infinity for both ALG and ${ALG}^{*}$ gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order $n$ and those of order 2.

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二次体积增长的引力瞬子

有两类已知的引力瞬子在无限远处具有二次体积增长，分别称为 ALG $\operatorname{ALG}$ 型和 ALG ∗ $\operatorname{ALG}^*$ 型。陈省身之前对 ALG $\operatorname{ALG}$ 类型的引力瞬子进行了分类。本文证明了 ALG ∗ ${rm ALG}^*$ 引力瞬子的分类定理。我们确定了 ALG 和 ALG ∗ ${rm ALG}^*$ 引力瞬子的拓扑结构，并证明了无穷大处 "均匀 "坐标的存在。我们还证明了阶数为 n $\mathfrak {n}$ 的 ALG 引力瞬子与阶数为 2 的 ALG 引力瞬子之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.