Duke Mathematical Journal

Branch points of Willmore surfaces

Ernst Kuwert and Reiner Schätzle

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We consider Willmore surfaces in R3 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 |A(x)|Cε|x|1+1/θ0ε,  ε>0, where θ0N is the maximal multiplicity. Examples of branched minimal surfaces show that this estimate is optimal up to the error ε>0

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Duke Math. J., Volume 138, Number 2 (2007), 179-201.

First available in Project Euclid: 5 June 2007

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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

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