Geodesic
Removability of point singularities of Willmore surfaces
Ernst Kuwert1 ; Reiner Schätzle2
1 Mathematisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany
2 Mathematisch-Naturwissenschaftliche Fakultät, Rheinische Friedrich-Wilhelms-Universität Bonn, 53115 Bonn, Germany
Annals of mathematics, Tome 160 (2004) no. 1, pp. 315-357.

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We investigate point singularities of Willmore surfaces, which for example appear as blowups of the Willmore flow near singularities, and prove that closed Willmore surfaces with one unit density point singularity are smooth in codimension one. As applications we get in codimension one that the Willmore flow of spheres with energy less than $8 \pi$ exists for all time and converges to a round sphere and further that the set of Willmore tori with energy less than $8 \pi – \delta$ is compact up to Möbius transformations.
DOI : 10.4007/annals.2004.160.315

Ernst Kuwert 1 ; Reiner Schätzle 2

1 Mathematisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany
2 Mathematisch-Naturwissenschaftliche Fakultät, Rheinische Friedrich-Wilhelms-Universität Bonn, 53115 Bonn, Germany 
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Ernst Kuwert; Reiner Schätzle. Removability of point singularities of Willmore surfaces. Annals of mathematics, Tome 160 (2004) no. 1, pp. 315-357. doi : 10.4007/annals.2004.160.315. http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.160.315/

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