We study the problem of the stability of the extremals of the potential energy functional. By the stability of an extremal surface we mean the sign-definiteness of its second variation. For estimating the second variation of the functional, we use the properties of the eigenvalues of symmetric matrices. Also, we prove an analog of Alexandrov’s Theorem on the variational property of a sphere.

中文翻译：

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关于势能泛函的稳定极值

我们研究势能泛函极值的稳定性问题。极值表面的稳定性是指其第二个变化的符号确定性。为了估计泛函的第二个变化，我们使用对称矩阵的特征值的性质。此外，我们证明了关于球体变分性质的亚历山德罗夫定理的模拟。