4 problems

Balmus–Montaldo–Oniciuc constant-mean-curvature conjecture. Any proper biharmonic submanifold in $\mathbb{S}^{m+1}$ is CMC.

Let $M$ be a non-minimal biharmonic submanifold of the unit sphere $S^n(1)$. Constant-mean-curvature conjecture. The mean curvature of $M$ is constant. The claim is a weaker statem…

Classification conjecture. The only proper biharmonic hypersurfaces in $\mathbb{S}^{m+1}$ are the open parts of hyperspheres $\mathbb{S}^m(1/\sqrt{2})$ or of the standard products…

Global Chen conjecture. Any complete biharmonic immersed submanifold in $\mathbb{E}^N$ is minimal.