Pointwise Expansion of Degenerating Immersions of Finite Total Curvature

Abstract Generalising classical result of Müller and Šverák (J. Differ. Geom. 42(2), 229-258, 1995), we obtain a pointwise estimate the conformal factor sequences immersions from unit disk complex plane uniformly bounded total curvature converging strongly outside concentration point towards branched for which quantization energy holds. We show that multiplicity associated to parameter becomes eventually constant an integer equal order branch limiting immersion. Furthermore, deduce $$C^0$$ C 0 convergence normal in neck regions. Finally, these improved quantizations hold Willmore surfaces precompact class, spheres arising as solutions min-max problems viscosity method.