A singular Yamabe problem on manifolds with solid cones

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-24 DOI:10.1515/acv-2022-0105

Juan Alcon Apaza, Sérgio Almaraz

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引用次数: 0

Abstract

We study the existence of conformal metrics on noncompact Riemannian manifolds with noncompact boundary, which are complete as metric spaces and have negative constant scalar curvature in the interior and negative constant mean curvature on the boundary. These metrics are constructed on smooth manifolds obtained by removing d-dimensional submanifolds from certain n-dimensional compact spaces locally modelled on generalized solid cones. We prove the existence of such metrics if and only if d > n - 2 2

{d>\frac{n-2}{2}}

. Our main theorem is inspired by the classical results by Aviles–McOwen and Loewner–Nirenberg, known in the literature as the “singular Yamabe problem”.

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具有实锥的流形上的奇异 Yamabe 问题

我们研究了具有非紧凑边界的非紧凑黎曼流形上共形度量的存在性，这些度量作为度量空间是完整的，在内部具有负常标量曲率，在边界上具有负常平均曲率。这些度量是在光滑流形上构造的，光滑流形是通过从某些以广义实心圆锥为局部模型的 n 维紧凑空间中移除 d 维子流形而得到的。我们证明了当且仅当 d > n - 2 2 {d>\frac{n-2}{2}} 时这种度量的存在。 .我们的主要定理受 Aviles-McOwen 和 Loewner-Nirenberg 的经典结果启发，在文献中被称为 "奇异 Yamabe 问题"。

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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.