TU Berlin Fakultät II
Institut für Mathematik
     

Constrained Willmore Surfaces

       

  

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       willmore-sphere DFG Schwerpunktprograms Globale Differentialgeometrie

Antragsteller: Prof. Dr. U. Pinkall joint project with Prof. Dr. F. Pedit (Tübingen).
Finanzierung: Deutsche Forschungsgemeinschaft (DFG)
Programm: Schwerpunktprogramm Globale Differentialgeometrie
Laufzeit: 2003 - 2009
Mitarbeiter: Dr. C. Bohle, Dr. G. P. Peters.

The Willmore functional or elastic bending energy of an immersion is a global invariant of fundamental importance in contemporary surface theory. Its applications range from the biophysics of membranes to string theory. In our project we investigate constrained Willmore surfaces, the critical points of Willmore functional restricted to the class of conformal immersions of a fixed Riemann surface. A motivation for the study of this constrained variational problem is the question for the optimal geometric realization of a given Riemann surface in 3--space. Examples of constrained Willmore surfaces include all constant mean curvature surfaces in space forms.

Recent Publications

  • Franz Pedit, Conformally immersed tori in 4-space of spectral genus zero, in Progress in Surface Theory (Oberwolfach, April 29-May 5, 2007). To appear in Oberwolfach Rep. (2007). [online]
  • Christoph Bohle, Constrained Willmore surfaces, in Progress in Surface Theory (Oberwolfach, April 29-May 5, 2007). To appear in Oberwolfach Rep. (2007). [online]
  • G. Paul Peters, Bryant Surfaces with Smooth Ends, in Geometrie (Oberwolfach, October 8-14, 2006), Oberwolfach Rep. 3 (2006), no. 4, 2733-2736. [online]
  • Christoph Bohle, On constrained Willmore tori in the 4-sphere, in Geometrie (Oberwolfach, October 8-14, 2006), Oberwolfach Rep. 3 (2006), no. 4, 2705-2708. [online]
  • Christoph Bohle, G. Paul Peters, and Ulrich Pinkall, Constrained Willmore Surfaces, preprint, math.DG/0411479.
  • Christoph Bohle, G. Paul Peters, Bryant Surfaces with smooth ends, preprint, math.DG/0411480.

Günter Paul Peters . 16.10.2007.