Constrained Willmore surfaces

• Antragsteller: Professor Dr. Alexander I. Bobenko
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2003 bis 2008
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 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-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1154: Globale Differentialgeometrie
• Beteiligte Person: Professor Dr. Ulrich Pinkall