Conformal invariant functionals of immersions of tori into R3

We show, that higher analogs of the Willmore functional, defined on the space of immersions M² → R³, where M² is a two-dimensional torus, R³ is the three-dimensional Euclidean space are invariant under conformal transformations of R³. This hypothesis was formulated recently by I.A. Taimanov. Higher analogs of the Willmore functional are defined in terms of the Modified Novikov-Veselov hierarchy. This soliton hierarchy is associated with the zero-energy scattering problem for the two-dimensional Dirac operator.