2 00 8 Constrained Willmore Surfaces

Constrained Willmore Surfaces

The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surf...

5 Constrained Willmore Surfaces

We develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ HdA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surfaces in space forms.

O ct 2 00 6 Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional ∗

ar X iv : m at h / 04 12 16 9 v 1 [ m at h . D G ] 8 D ec 2 00 4 TABLEAUX OVER LIE ALGEBRAS , INTEGRABLE SYSTEMS , AND CLASSICAL SURFACE THEORY

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, projective minimal surfaces, and other classical soliton surfaces. Completely integrable equations suc...

ar X iv : m at h / 05 03 70 7 v 2 [ m at h . D G ] 1 4 N ov 2 00 5 Surfaces in three - dimensional Lie groups ∗

In the present paper we extend the methods of the Weierstrass (or spinor) representation of surfaces in R [10, 11] and SU(2) = S [12] for surfaces in the three-dimensional Lie groups Nil , S̃L2, and Sol endowed with the so-called Thurston’s geometries [9]. The main feature of this approach is that the geometry of a surface is related to the spectral properties of the corresponding Dirac operator...