具有康托尔端点的双曲空间和德西特空间中的 $$text {CMC-1}$$ 曲面

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Ildefonso Castro-Infantes, Jorge Hidalgo
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引用次数: 0

摘要

我们证明,在每一个紧凑黎曼曲面 M 上,都有一个康托集(C 子集 M),使得(M{ \setminus }C\)允许一个适当的保角恒定平均曲率一(\(\text {CMC-1}\))浸入双曲 3 空间(\mathbb {H}^3)。此外,我们还得到每个有边界的黎曼曲面都有一个几乎合适的(\text {CMC-1})面进入德西特 3 空间(\mathbb {S}_1^3\)、并且我们证明了在每一个紧凑黎曼曲面M上,都有一个康托集(C子集M),使得(M{setminus } C\ )有一个几乎合适的(text {CMC-1})面进入(mathbb {S}_1^3\)。这些结果来自于我们在本文中建立的针对 \(\mathbb {C}^2 \times \mathbb {C}^*\) 中全形空曲线的不同均匀逼近定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

$$\text {CMC-1}$$ Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends

$$\text {CMC-1}$$ Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends

We prove that on every compact Riemann surface M, there is a Cantor set \(C \subset M\) such that \(M{ \setminus }C\) admits a proper conformal constant mean curvature one (\(\text {CMC-1}\)) immersion into hyperbolic 3-space \(\mathbb {H}^3\). Moreover, we obtain that every bordered Riemann surface admits an almost proper \(\text {CMC-1}\) face into de Sitter 3-space \(\mathbb {S}_1^3\), and we show that on every compact Riemann surface M, there is a Cantor set \(C \subset M\) such that \(M {\setminus } C\) admits an almost proper \(\text {CMC-1}\) face into \(\mathbb {S}_1^3\). These results follow from different uniform approximation theorems for holomorphic null curves in \(\mathbb {C}^2 \times \mathbb {C}^*\) that we also establish in this paper.

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来源期刊
Accounts of Chemical Research
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.
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