Analysis of constrained Willmore surfaces

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This paper investigates the regularity of constrained Willmore immersions into ℝm≥3 locally around both “regular” points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions for the immersion and its first and second derivatives, given in terms of residues computed as circulation integrals. We deduce explicit “point removability” conditions ensuring that the immersion is smooth. Our results apply in particular to Willmore immersions and to parallel mean curvature immersions in any codimension.

Original languageEnglish
Pages (from-to)1513-1552
Number of pages40
JournalCommunications in Partial Differential Equations
Issue number10
Publication statusPublished - 2 Oct 2016


  • Conformal Willmore equation
  • regularity
  • singular behaviour
  • singularity removability
  • Willmore energy

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