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Constrained Willmore surfaces

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
Beteiligte Person Professor Dr. Ulrich Pinkall
 
 

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