Existence and Stability of α- harmonic Maps
Abstract
In this paper, we first study the α-energy functional, Euler-Lagrange operator and α-stress energy tensor. Second, it is shown that the critical points of α- energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α-harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α- harmonic maps are minimal submanifolds. Then, the stability of any α-harmonic map from a Riemannian manifold to a Riemannian manifold with non-positive Riemannian curvature is demonstrated. Finally, the instability of α-harmonic maps from a compact manifold to a standard unit sphere is investigated.
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