论文标题
最大化雅各比操作员的第一个特征值
Maximizing the first eigenvalue of the Jacobi operator
论文作者
论文摘要
我们认为雅各比操作员定义在浸入欧几里得空间中具有相同体积的单位球体的封闭式的超曲面上。我们为欧几里得球体的Willmore功能的经典结果显示了局部概括。结果，我们证明了欧几里得球中雅各比操作员的第一个特征值是局部最大值，并且该结果是$ \ mathbb {r}^3 $和零属的封闭式表面空间中的全球结果。
We consider the Jacobi operator, defined on a closed oriented hypersurfaces immersed in the Euclidean space with the same volume of the unit sphere. We show a local generalization for the classical result of the Willmore functional for the Euclidean sphere. As a consequence, we prove that the first eigenvalue of the Jacobi operator in the Euclidean sphere is a local maximum and this result is a global one in the closed oriented surfaces space of $\mathbb{R}^3$ and genus zero.
