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

Wei, Guodong

doi:10.1090/proc/14614

An Hélein’s type convergence theorem for conformal immersions from $\mathbb {S}^{2}$ to manifold
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Proc. Amer. Math. Soc. 147 (2019), 4969-4977 Request permission

Abstract:

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

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