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.

中文翻译：

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可校准 Cheeger Serrin 域上的无界周期性常平均曲率图

我们证明了表征特定类别 Serrin 域的一般结果，作为无界和周期性恒定平均曲率图的支持。我们应用这个结果来证明一系列无界周期性常平均曲率图的存在，每个图都由 Serrin 域支持并与其边界正交相交，直至平移。我们还表明，底层的 Serrin 域是可校准的，并且 Cheeger 在适当的意义上是可校准的，并且它们求解 1-拉普拉斯方程。