Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions. © 2022 Wiley Periodicals LLC.

中文翻译：

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作为毛细现象的奇异极限的高原问题

通过引入具有同伦跨越条件的毛细管问题，将平衡状态的皂膜建模为总体积较小的区域，而不是表面。这种观点在经典高原问题中引入了一个长度尺度，该长度尺度又在体积消失极限中恢复。这种面积最小化超曲面的近似导致了 Plateau 问题的基于能量的选择原则，指出了通过简单地查看最小曲面无法访问的肥皂膜的物理特征，并提出了几个具有挑战性的问题。© 2022 威利期刊有限责任公司。