2 problems

De Giorgi's finite-traces conjecture. For every $x\in\Omega$, the set $E(x)$ has finite cardinality $\alpha(x)\leq N+1$.

Let $(u,K)$ be a reduced global minimizer in $\mathbb R^3$, meaning a Mumford–Shah global minimizer whose singular set $K$ is reduced, and suppose that $K$ is contained in a plane…