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

Guodong Wei | Zendy

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An 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) - mathematics , conformal map , type (biology) , manifold (fluid mechanics) , pure mathematics , convergence (economics) , mathematical analysis , biology , economics , ecology , engineering , economic growth , mechanical engineering

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.

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