An Hélein’s type convergence theorem for conformal immersions from 𝕊² to manifold

Abstract

In this short paper, we establish an Hélein’s type convergence theorem for conformal immersions from S 2 \mathbb {S}^{2} to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of ∫ | A | 2 d μ \int |A|^{2} d\mu for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.