The classical Helein convergence theorem established by F. Helein has played an important role in the analysis of 2-dimensional conformally invariant problems. In this talk, I will present an Helein’s type convergence theorem for conformal immersions from S2 to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of 
for immersed 2-spheres in compact 3-manifold under certain conditions due to E. Kuwert, A. Mondino and J. Schygulla (2014) to higher codimensions.
