ABSTRACT
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 [1, 5, 13, 19], a zero-curvature formulation follows [5]. Deformations on the level of harmonic maps prove to give rise to deformations on the level of surfaces, with the definition of a spectral deformation [5, 8] and of a Bäcklund transformation [9] of Willmore surfaces into new ones, with a Bianchi permutability between the two [9]. This text is dedicated to a self-contained account of the topic, from a conformally-invariant viewpoint, in Darboux’s light-cone model of the conformal n-sphere.
