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arXiv · 1801.06786

Weak convergence of branched conformal immersions with uniformly bounded areas and Willmore energies

Guodong Wei
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Abstract

In this paper, we firstly extend Theorem 5.1.1 in \cite {Helein} due to H\'elein to a rescaled branched conformal immersed sequence(c.f. Theorem 1.5). By virtue of this local convergence theorem, we study the blowup behavior of a sequence of branched conformal immersions of closed Riemannian surface in $\mathbb{R}^{n}$ with uniformly bounded areas and Willmore energies. Furthermore, we prove that the integral identity of Gauss curvature is true.

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Guodong Wei. 2018-01-21. Weak convergence of branched conformal immersions with uniformly bounded areas and Willmore energies. https://arxiv.org/abs/1801.06786

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