3 problems

Trudinger–Wang's conjecture. If $n\leq 9$, then $u$ is an elliptic quadratic polynomial. If $n\geq 10$, then there exists a smooth, locally uniformly convex solution of the equatio…

Let $u\colon\mathbb{R}^2\to\mathbb{R}$ be smooth and locally uniformly convex, and suppose its graph is an affine maximal graph, meaning that $u$ satisfies the affine maximal surfa…

Let $\Sigma^3\subset\mathbb{R}^4$ be a complete immersed $2$-sided stable minimal hypersurface. Schoen's Bernstein conjecture. $\Sigma$ is flat. The conjecture extends the Bernstei…