Duke Mathematical Journal
- Duke Math. J.
- Volume 138, Number 2 (2007), 179-201.
Branch points of Willmore surfaces
We consider Willmore surfaces in with an isolated singularity of finite density at the origin. We show that locally, the surface is a union of finitely many multivalued graphs, each with a unique tangent plane at zero and with second fundamental form satisfying where is the maximal multiplicity. Examples of branched minimal surfaces show that this estimate is optimal up to the error
Duke Math. J., Volume 138, Number 2 (2007), 179-201.
First available in Project Euclid: 5 June 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A05: Surfaces in Euclidean space
Secondary: 53A30: Conformal differential geometry 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]
Kuwert, Ernst; Schätzle, Reiner. Branch points of Willmore surfaces. Duke Math. J. 138 (2007), no. 2, 179--201. doi:10.1215/S0012-7094-07-13821-3. https://projecteuclid.org/euclid.dmj/1181051029