Veronese曲面的Willmore稳定性

The Willmore stability of the Veronese surface

设x0:M^m→S^n是球空间Sn中的正则子流形,计算x0的共形体积泛函的第一和第二变分公式,并且通过计算证明了S4中Veronese曲面是Willmore稳定的.

Let x0： Mm→Snis a space-like submanifold in the sphere space Sn. We calculated again the first and second variation formulae of the conformal volume functional of x0,and we also calculated the Willmore stability of the Veronese surface.