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Geometric Analysis and Partial Differential Equations Seminar
October 17, 2013 @ 10:30 am - 11:30 pm
Dr. Yann Bernard (Freiburg University)
Conservation laws for the Willmore functional and associated results
Using Noether’s theorem, we will show that the Willmore equation can be recast in a system of equations in divergence form. Particularly suited for “critical” analysis, this system will in particular be used to understand the behavior of a Willmore immersion near a point-singularity. We will develop local asymptotic expansions for the immersion, its first and second derivatives in terms of residues computed as circulation integrals around the point singularities. We will deduce explicit “point removability” conditions ensuring the smoothness of the immersion.