Yingbo Han, Shuxiang Feng and Wei Zhang: Liouville theorems for weakly $F$-stationary maps with potential, p.435-450

Abstract:

In this paper, we introduce the notion of weakly $F$-stationary map with potential which is a critical point of the functional $\Phi_{F,H}$ with respect to variations in the domain. It is a generalization of $F$-stationary maps with potential. We obtain some Liouville theorems for these maps under some curvature conditions of the domain manifolds and some conditions on $H$. We obtain similar theorems for maps obeying a class of integral equations involving the stress-energy tensor.

Key Words: Weakly $F$-stationary map with potential, Liouville theorem, stress-energy tensor.

2000 Mathematics Subject Classification: Primary: 58E20;
Secondary: 53C21.

Download the paper in pdf format here.