Open AccessAn Hélein’s type convergence theorem for conformal immersions from 𝕊² to manifold
Author(s) -
Guodong Wei
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14614
Subject(s) - algorithm , artificial intelligence , convergence (economics) , type (biology) , computer science , geology , paleontology , economic growth , economics
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.