可校准切格-塞林域上的无界周期恒均值曲率图

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-01-25 DOI:10.1007/s00013-023-01960-0

Ignace Aristide Minlend

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引用次数: 0

摘要

我们证明了一个一般结果，它描述了作为无界周期性均值曲率恒定图的支撑的一类特定塞林域的特征。我们应用这一结果证明了无界周期性恒均值曲率图形族的存在，每个图形都由一个塞林域支撑，并与其边界正交，直至平移。我们还证明了底层 Serrin 域在适当的意义上是可校准的和 Cheeger 的，并且它们解决了 1-Laplacian 方程。

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Unbounded periodic constant mean curvature graphs on calibrable Cheeger Serrin domains

We prove a general result characterizing a specific class of Serrin domains as supports of unbounded and periodic constant mean curvature graphs. We apply this result to prove the existence of a family of unbounded periodic constant mean curvature graphs, each supported by a Serrin domain and intersecting its boundary orthogonally, up to a translation. We also show that the underlying Serrin domains are calibrable and Cheeger in a suitable sense, and they solve the 1-Laplacian equation.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.