Constrained Willmore surfaces

• Applicant: Professor Dr. Alexander I. Bobenko
• Subject Area: Mathematics
• Term: from 2003 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5406556

We want to study a class of surfaces in 3-space, the so-called "constrained Willmore surfaces". These are defined as the critical points of the Willmore function when only those variations are allowed that preserve the conformal type of the surface. This class of surfaces is invariant under Möbius transformations of the ambient space. Examples include constant mean curvature surfaces in Euclidean space, hyperbolic space and the 3-sphere. Our main interest is the construction and classification of new compact examples, mainly topological spheres and tori. We hope to obtain explicit formulas for all constrained Willmore spheres and tori from a soliton theoretic approach.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry
• Participating Person: Professor Dr. Ulrich Pinkall