Stability of hypersurfaces of constant mean curvature with free boundary in two parallel hyperplanes
Stability of hypersurfaces of constant mean curvature with free boundary in two parallel hyperplanes
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DOI：
10.14495/jsiaml.15.9
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Miyuki Koiso;U. Miyamoto
中科院分区：
文献类型：
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作者：
Miyuki Koiso;U. Miyamoto
常平均曲率曲面是具有体积约束的面积的临界点。它们是肥皂泡和微小液滴表面的数学模型。CMC曲面被称为是稳定的，如果第二个变化的面积是非负的所有体积保持变化满足给定的边界条件。本文研究了一般欧氏空间中可能在两个平行超平面上具有边界的CMC超曲面的稳定性。我们首次揭示了无自相交的平衡超曲面在所有维度上的稳定性。数值计算有助于分析。
Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second variation of the area is nonnegative for all volume-preserving variations satisfying the given boundary condition. In this paper, we examine the stability of CMC hypersurfaces in general Euclidean space possibly having boundaries on two parallel hyperplanes. We reveal the stability of equilibrium hypersurfaces without self-intersection for the first time in all dimensions. The analysis is assisted by numerical computations.