Akutagawa–Maeta conjecture for complete biharmonic Euclidean submanifolds

Let $M$ be a complete submanifold of Euclidean space $\mathbb{E}^n$. An isometric immersion $\phi:(M,g)\rightarrow\mathbb{E}^n$ is biharmonic when its bitension field satisfies $\tau_2(\phi)=0$, and $M$ is minimal when its mean curvature vanishes. Akutagawa–Maeta conjecture. Every complete biharmonic submanifold in $\mathbb{E}^n$ is minimal. This is the global, completeness-assuming reformulation of Chen's conjecture. The source presents it as a problem in global differential geometry and does not give a resolution of the general case.