Willmore surfaces are the extremals of the Willmore functional (possibly under a constraint on the conformal structure). With the characterization of Willmore surfaces by the (possibly perturbed) harmonicity of the mean curvature sphere congruence [Blaschke, Ejiri, Rigoli, Burstall-Calderbank], a zero-curvature formulation follows [Burstall-Calderbank]. Deformations on the level of harmonic maps prove to give rise to deformations on the level of surfaces, with the definition of a spectral… Expand

This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric… Expand

so the two functional differ by a constant. The functional i^(X) has the advantage that its integrand is nonnegative and vanishes exactly at the umbilic points of the immersion X. Obviously iT(X) = 0… Expand

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $${\mathcal{W}} = \int H^2$$ under compactly supported infinitesimal… Expand

In Part I, we develop the notions of a Moebius structure and a conformal Cartan geometry, establish an equivalence between them; we use them in Part II to study submanifolds of conformal manifolds in… Expand

The special isothermic surfaces, discovered by Darboux in connection with deformations of quadrics, admit a simple explanation via the gauge-theoretic approach to is othermic surfaces and extend the theory to arbitrary codimension.Expand