Constrained Willmore surfaces

• Antragsteller: Professor Dr. Franz Pedit; Professor Dr. Ulrich Pinkall
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2005 bis 2011
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 15028839

The Willmore functional or elastic bending energy W — ∫ H2 of an immersion is a global invariant of fundamental importance in contemporary surface theory and applications ranging from the biophysics of membranes to string theory. We investigate the so-called constrained Willmore surfaces which are conformal immersions of a Riemann surface that are critical points of VV under compactly supported infinitesimal conformal variations. During the third period of the project the focus of our investigations is on finding estimates for the Willmore energy of constrained Willmore tori. These can all be constructed by methods of complex algebraic geometry which suggests that the fundamental algebraic geometric invariants like the degree of certain appendant holomorphic maps or the genus of the so called spectral curve should be related to the Willmore energy of the immersion. For several special cases we can establish such a link and our plan is to generalize the obtained estimates to arbitrary constrained Willmore tori.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1154: Globale Differentialgeometrie