4 problems

Minimal immersion conjecture. The immersion $f$ must be totally geodesic.

Asymptotically Euclidean immersion conjecture. There exists an asymptotically Euclidean isometric immersion

Piecewise smooth immersion conjecture. There exists a piecewise smooth isometric immersion

Let $M^{n_1}_1$ and $M^{n_2}_2$ be Riemannian manifolds. Suppose that $M^{n_1}_1$ can be locally isometrically immersed in $\mathbb{R}^{n_1+p_1}$ but in no lower-dimensional Euclid…