Plateau's Problem as a Singular Limit of Capillarity Problems

被引：8
作者：
King, Darren [1 ]
Maggi, Francesco [1 ]
Stuvard, Salvatore [1 ]
机构：
[1] Univ Texas Austin, Dept Math, 2515 Speedway,Stop C1200, Austin, TX 78712 USA
来源：
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2023年 / 76卷 / 06期
关键词：
PRESCRIBED MEAN-CURVATURE; EXISTENCE; MINIMIZATION; THEOREMS; CURRENTS;
D O I：
10.1002/cpa.21951
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (c) 2020 Wiley Periodicals LLC
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收藏
页码：1139 / 1207
页数：69
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