6 problems

Simon's conjecture. One has

Taimanov's conformal invariance conjecture. The higher Willmore functionals and the spectral curve for tori in ${\mathbb R}^3$ are conformally invariant.

Let $\Sigma$ be a sphere immersed in $\mathbf{R}^3$, let $\mathcal D$ be a Dirac operator acting on a spinor bundle over $\Sigma$, and let $\mathcal W(\Sigma)$ denote the Willmore…

Let the Willmore functional be defined on immersed tori, and consider the deformations generated by equation (6) of the source. Stationarity conjecture. The minima of this function…

Let $M^{2}\subset\mathbb{S}^{3}(1)$ be an embedded closed surface of genus one, and suppose that the curvature endomorphism satisfies $\Re|_{\slashed{E}}=0$. Let $\bar{\Gamma}_{1}$…

Finite-type conjecture for Willmore tori. Every Willmore torus is of finite type.