嘉当魔术公式与肥皂膜结构
Cartan's Magic Formula and Soap Film Structures
摘要：
肥皂膜实际上是一种薄的固体流体，由两个方向相反的表面包围。这是自然的模型的电影使用一个多面体的每一面。两个问题是得到多面体的两侧是在同一个地方，而不相互抵消了，并建立模型的三重路口，而不引入额外的边界组件。我们使用chainlet几何创建偶极细胞和质量细胞，实现这些目标，并忠实地模拟所有可观察到的肥皂膜和气泡。我们引入了一个新的范数，并证明了面积的下半连续性。一个几何版本的嘉当魔术公式提供了必要的边界连贯性。
英文摘要：
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place without canceling each other out and to model triple junctions without introducing extra boundary components. We use chainlet geometry to create dipole cells and mass cells which accomplish these goals and model faithfully all observable soap films and bubbles. We introduce a new norm on chains of these cells and prove lower semicontinuity of area. A geometric version of Cartan's magic formula provides the necessary boundary coherence.
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