Stabilities of F-stationary maps

Abstract

An F-stationary map is a critical point of the F-energy with respect to variations in the domain. It is a generalization of F-harmonic maps. In [11, 10], we discuss the theorems of Liouville type and the monotonicity of F-stationary maps. In this paper, we discuss the stabilities of F-stationary maps from submanifolds of spheres and the Euclidean spaces.