The complete Chen conjecture for biharmonic submanifolds in Euclidean space

Let $M$ be a complete isometrically immersed submanifold of Euclidean space $\mathbb{E}^N$. It is biharmonic when its immersion is a biharmonic map.

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

This is presented as a global reformulation of Chen's conjecture, obtained by imposing completeness. The supplied text does not report a resolution of this complete version, so its general status remains open there.