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

2018/01/21 by Guodong Wei, Wei, Guodong
Mathematics · #35J35 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1801.06786

openalex publication_date 2018/01/21 · openalex created_date 2018/02/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we firstly extend Theorem 5.1.1 in \cite Helein due to Hélein 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 ℝⁿ with uniformly bounded areas and Willmore energies. Furthermore, we prove that the integral identity of Gauss curvature is true.

Related

• Variational Principles for immersed Surfaces with L²-bounded Second\n Fundamental Form
• Higher Regularity of Weak Limits of Willmore Immersions I
• Limits of conformal immersions under a bound on a fractional normal\n curvature quantity
• Sequences of Smooth Global Isothermic Immersions
• Bubble tree of a class of conformal mappings and applications to Willmore functional