liouville-type theorems for sacks-uhlenbeck biharmonic maps

Let (m^{m},g) be a complete riemannian manifold, (p^{p},varrho) be a riemannian manifold with ricci ^{p}leq 0 and phi:(m,g) longrightarrow (p,varrho) be a sacks-uhlenbeck biharmonic map for beta >1, namely, a critical point of the functional e_{beta,2}(phi):=int _{m}(1+mid tau(phi) mid ^{2})^{beta}dv _{g}, where tau(phi) is the tension field of phi . we prove a liouville-type theorem for sacks-uhlenbeck biharmonic map phi .