Existence of static vacuum extensions with prescribed Bartnik boundary data

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-29 DOI:10.4310/cjm.2022.v10.n1.a1

Z. An, Lan-Hsuan Huang

引用次数: 6

Abstract

We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.

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给定Bartnik边界数据的静态真空扩展的存在性

我们证明了欧几里德空间中任意星形超曲面或一般摄动超曲面族上具有与诱导边界数据接近的任意规定Bartnik边界数据的渐近平坦静态真空度量的存在性和局部唯一性。证实了大类别边界数据的Bartnik静态扩展猜想的部分存在性，得到的静态真空度规在欧几里德度规的邻域内具有几何唯一性。

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

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.