Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by “collapsed” minimal surfaces. We prove here that collapsing only occurs if the mean curvature/pressure of the bulky regions is negative, and that, when this last property holds, the whole soap film lies in the convex hull of its boundary wire frame.

中文翻译：

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肥皂膜毛细管模型中的塌陷和凸包特性

在毛细作用理论的框架内研究悬挂在金属丝框架上的肥皂膜。已知相应变分问题中的最小化器由具有恒定平均曲率/压力边界的正体积区域组成，可能由“折叠”最小表面连接。我们在这里证明只有当大块区域的平均曲率/压力为负时才会发生塌陷，并且当最后一个属性成立时，整个肥皂膜位于其边界线框的凸包中。