关于Graham-Witten能量的二阶变分
On the second variation of the Graham-Witten energy
摘要：
面积重整化方法给出了共形流形中偶数维闭子流形的一个不变量，我们称之为Graham-Witten能量，它是经典Willmore能量的推广.本文给出了Einstein流形中极小子流形上该能量的二阶变分的一个显式公式。作为应用，我们证明了单位球面中的偶数维全测地球面是具有非负二阶变分的Graham-Witten能量的临界点.
英文摘要：
The area renormalization procedure gives an invariant of even-dimensional closed submanifolds in a conformal manifold, which we call the Graham-Witten energy, and it is a generalization of the classical Willmore energy. In this paper, we obtain an explicit formula for the second variation of this energy at minimal submanifolds in an Einstein manifold. As an application, we prove that the even-dimensional totally geodesic spheres in the unit sphere are critical points of the Graham-Witten energy with non-negative second variation.
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