论文标题
具有限制平均曲率的超曲面的异含量残基和中尺度平坦标准
Isoperimetric residues and a mesoscale flatness criterion for hypersurfaces with bounded mean curvature
论文作者
论文摘要
对于大容量$ v \ to \ infty $，我们在外部等级问题中获得了最小化器中的最小化结果的完整分辨率结果。这是通过研究高原类型问题的自由边界（无论是紧凑型障碍物还是在无穷大）中实现，该问题用于识别能量扩展中的第一个依赖障碍物（称为{\ IT等级等级），例如$ v \ to \ fos to \ iffty $，外部等等等距等问题。分析等值残基的一个关键工具是针对具有界平均曲率的高空曲面的新的中尺度平坦标准，我们作为源自具有孤立奇异性的最小表面理论的思想的发展而获得的。
We obtain a full resolution result for minimizers in the exterior isoperimetric problem with respect to a compact obstacle in the large volume regime $v\to\infty$. This is achieved by the study of a Plateau-type problem with free boundary (both on the compact obstacle and at infinity) which is used to identify the first obstacle-dependent term (called {\it isoperimetric residue}) in the energy expansion, as $v\to\infty$, of the exterior isoperimetric problem. A crucial tool in the analysis of isoperimetric residues is a new mesoscale flatness criterion for hypersurfaces with bounded mean curvature, which we obtain as a development of ideas originating in the theory of minimal surfaces with isolated singularities.
