论文标题
在肥皂膜毛细管模型中塌陷和凸壳特性
Collapsing and the convex hull property in a soap film capillarity model
论文作者
论文摘要
在毛细血管理论的框架中研究了从电线框架上悬挂的肥皂膜。已知相应的变分问题中的最小化器由正体积区域组成，具有恒定平均曲率/压力的边界，可能通过“折叠”的最小表面连接。我们在这里证明，仅当笨重区域的平均曲率/压力为负时，就会发生崩溃，并且当最后一个属性成立时，整个肥皂膜都位于其边界线框架的凸面上。
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.
