Liouville theorems of stable F-harmonic maps for compact convex hypersurfaces

Abstract

Let M be a compact convex hypersurface in Rnþ1. In this paper, we proved firstly that if the principal curvatures li of M n satisfy 0 < l1 a a ln and ln < Pn 1 j1⁄41 lj , then there exist no nonconstant stable F -harmonic map between M and a compact Riemannian manifold when (1.2) or (1.3) holds (Theorem 1). This is a generalization or unification of the corresponding results for several varieties of harmonic map. Then, when the target manifold is d-pinched, using a new estimate method, we obtain the Liouville-type theorem (Theorem 2) for stable F -harmonic map, which improves the results of M. Ara in [2].