正拼挤流形的F-调和映射

Abstract

设M~n(n≥3)是R~(n+1)中紧致凸超曲面,本文证明了:若F″≤0且M的n个主曲率λ_i满足0<λ_i<1/2∑_(j=1)~nλ_j,则M~n和任何紧致黎曼流形之间的稳定F-调和映射必为常值映射.

Let Mn (n ≥ 3) be a compact convex hypersurface in Rn+1. In this paper, we prove that if F" ≤ 0 and the principal curvature λi of M satisfies: , (?)i m then there is no rionconstant stable F-harmonic map between M and a compact Riemannian manifold.