位势p-调和映射的变分计算

The variational calculation of potential p-Harmonic maps

讨论p-H-调和映射的一阶和二阶变分计算,作为应用,我们利用变分计算公式证明了一个稳定性定理:设Mm是一紧致无边的黎曼流形,Sn是n维单位球面.如果u是从Mm到Sn的稳定的p-H-调和映射(n>p),并且HessH≤0,则u是常值映射.

In this paper, we discuss the first and second variations of p-H-Harmonic maps. As an application of the Variational formulas, we prove a stable theorem: Let M^m be a compact Riemannian manifold, S^n is of n dimensional unit sphere. If u is a stable p-H-Harmonic map(n>p), and HessH≤0, then u is constant.