论文标题
关于弹性模量的Euler-Plateau问题
Regarding the Euler-Plateau Problem with Elastic Modulus
论文作者
论文摘要
我们研究了Euler-Plateau能量与弹性模量的平衡构型，该模量将Euler-Plateau类型的能量功能与总曲率项相结合，通常是在模型中用于生物膜自由能。结果表明，该能量的潜在最小化器高度取决于物理刚性参数的选择，并且临界表面的面积可以完全从其边界数据中计算出来。当弹性模量不会消失时，表明轴向对称的临界浸入和磁盘类型的临界浸入必须是面积受面积约束的弹性e界的平面域。还讨论了具有多个边界成分和无限制属的拓扑属零属的病例，并进行了对大地扭转的控制，并给出了足够的条件，在这些情况下，它们确定了相同的结论。
We study equilibrium configurations for the Euler-Plateau energy with elastic modulus, which couples an energy functional of Euler-Plateau type with a total curvature term often present in models for the free energy of biomembranes. It is shown that the potential minimizers of this energy are highly dependent on the choice of physical rigidity parameters, and that the area of critical surfaces can be computed entirely from their boundary data. When the elastic modulus does not vanish, it is shown that axially symmetric critical immersions and critical immersions of disk type are necessarily planar domains bounded by area-constrained elasticae. The cases of topological genus zero with multiple boundary components and unrestricted genus with control on the geodesic torsion are also discussed, and sufficient conditions are given which establish the same conclusion in these cases.
