Balmus–Montaldo–Oniciuc constant-mean-curvature conjecture for proper biharmonic submanifolds

Let $\mathbb{S}^{m+1}$ be the unit sphere, and consider a proper biharmonic submanifold of it. A submanifold is CMC when its mean curvature is constant.

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

The conjecture is presented as the second of two conjectures concerning biharmonic hypersurfaces and submanifolds in spheres. The supplied text does not state whether it has been resolved.