2 problems

Barycenter conjecture. In higher dimensions, the point of tangency is the barycenter of $U$.

Let $W$ be a compact manifold of dimension $n\geq m$, let $u\in C^\infty(W,\mathbb{R}^m)$, and let $\theta$ be its Pareto critical set, with $\theta_S$ denoting the singular part o…