2016/10/20 by Chong, Tian, Bofeng Cheng, Cheng, Bofeng +4
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1610.06301
In this paper, we consider the smooth map from a Riemannian manifold to the standard Euclidean space and the p-Ginzburg-Landau energy. Under suitable curvature conditions on the domain manifold, some Liouville type theorems are established by assuming either growth conditions of the p-Ginzburg-Landau energy or an asymptotic condition at the infinity for the maps. In the end of paper, we obtain the unique constant solution of the constant Dirichlet boundary value problems on starlike domains.