4 problems

Ren–Wang's concavity conjecture. Their concavity inequality should hold for all $k$ satisfying

Existence and uniqueness conjecture. There exists a unique $k$-admissible solution $u$ satisfying

Let $\phi\colon S^1\times\mathbb{R}\to\mathbb{R}^{1+3}$ be a smooth, proper, timelike maximal immersion, and consider evolutions of generic closed curves in higher codimension. Gen…

Let $n\geq 3$ and consider timelike extremal cylinders, namely timelike extremal immersions of $\mathbb R\times\mathbb S^1$ into $(1+n)$-dimensional flat Minkowski space. Higher-di…