5 problems

Chen–Maeta conjecture. Every $r$-harmonic submanifold of ${\mathbb R}^n$ is minimal.

Existence conjecture. The equation for $r$-harmonic curves admits solutions with non-constant geodesic curvature

Let $M^m$ be a hypersurface in the unit sphere ${\mathbb S}^{m+1}$. Here $r$-harmonic and $ES$-$r$-harmonic refer to the notions used in the source, and proper means $r$-harmonic b…

Let $M^m$ be a hypersurface in the unit sphere ${\mathbb S}^{m+1}$. Here $r$-harmonic and $ES$-$r$-harmonic refer to the notions used in the source, $f$ denotes the mean curvature…

Let $M^m(c)$ be an $m$-dimensional space form of constant sectional curvature $c$, let $N^{m-1}$ be a manifold, and let $\varphi:M^m(c)\to N^{m-1}$ be a Riemannian submersion. Subm…