关于指数调和映射的不稳定性

On the unstability of exponentially harmonic maps

设Mm Rm+1为紧致凸超曲面,m个主曲率0<λ1≤λ2≤…≤λm满足:λm<λ1+λ2+…+λm-1,证明如果::M→N为稳定的指数调和映射,且,则,为常值映射.

Let Mn be a compact convex hypersurface in R^n＋1. The principal curvature λ i of M Satisfies：0〈λ1≤λ2≤…≤λm andλm〈λ1＋λ2＋…＋λm-1. In this paper, We prove that if ｜dФ｜^2〈1/2λm^2mini{λi（m∑j=1λj-2λi）},then there is no nonconstant stable exponentially harmonic maps from M to any Riemannian manifolds.