Soap films with gravity and almost-minimal surfaces
Soap films with gravity and almost-minimal surfaces
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具有重力和几乎最小表面的肥皂膜
DOI：
10.3934/dcds.2019236
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Salvatore Stuvard
中科院分区：
文献类型：
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作者：
F. Maggi;A. Scardicchio;Salvatore Stuvard
在研究悬挂在线框上的肥皂膜的平衡方程的基础上，证明了平均曲率渐近为零且边界固定或收敛的曲面的紧性定理。特别地，我们得到了关于给定边界所跨越的极小曲面的充分几何条件，以表示几乎极小曲面序列的所有可能极限。最后，我们给出了一个几乎极小曲面到其极限极小曲面距离的一些精确的定量估计。
Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we obtain sufficient geometric conditions for the minimal surfaces spanned by a given boundary to represent all the possible limits of sequences of almost-minimal surfaces. Finally, we provide some sharp quantitative estimates on the distance of an almost-minimal surface from its limit minimal surface.