Chen's conjecture on biharmonic submanifolds in Euclidean spaces

Let $M$ be a biharmonic submanifold of a Euclidean space. Chen's conjecture. Every such submanifold is minimal. Chen, Ishikawa, and Jiang proved the claim for biharmonic surfaces in $\mathbb{E}^3$, and subsequent work established it for several low-dimensional hypersurface cases; the case of hypersurfaces in $\mathbb{E}^{n+1}$ for $n\geq 6$ remains open.