Analysis of constrained Willmore surfaces

作者：Bernard Yann^*

来源：Communications in Partial Differential Equations, 2016, 41(10): 1513-1552.

DOI：10.1080/03605302.2016.1222543

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

This paper investigates the regularity of constrained Willmore immersions into (m3) 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.

• 出版日期2016