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

• 作者: Guodong Wei
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: Articles
• 页码范围: 781-798
• 页数: 18页
• 语种: 英文

摘要

In this paper,we first extend the classical Hé1ein's convergence theorem to a sequence of rescaled branched conformal immersions.By virtue of this local convergence theorem,we study the blow-up behavior of a sequence of branched conformal immersions of a closed Riemann surface in Rn with uniformly bounded areas and Willmore energies.Furthermore,we prove that the integral identity of Gauss curvature is true.