Conformal invariance of higher DSII integrals for surfaces

Let the DSII hierarchy be the integrable hierarchy governing deformations of surfaces immersed in $\mathbb{R}^4$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$ via generalized Weierstrass representations. Its higher integrals of motion define functionals on these surfaces. Conformal invariance conjecture. Higher integrals of motion for the DSII hierarchy are functionals on surfaces in $\mathbb{R}^4$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$ that are invariant under conformal transformations in these spaces. The Willmore functional is already known to have this conformal invariance, motivating the proposed extension to the higher integrals of motion; no resolution is given here.