7 problems

Let $\mathcal A$ be a complete abelian left-symmetric algebra (LSA) with a nondegenerate Hessian-type inner product. Let $\operatorname{sDer}(\mathcal A)$ denote its space of infin…

Cayley hypersurface characterisation conjecture. Then, in a suitable affine coordinate system, $\Sigma$ is given by the Cayley hypersurface equation.

Semi-parallelism and parallelism conjecture. The two conditions are equivalent:

Izumiya's Lagrangian stability conjecture. Germs of generic Blaschke affine normal congruences at any point are Lagrangian stable.

Trudinger–Wang's conjecture. The first boundary value problem has a unique smooth solution $u$ if $\phi$ is affine mean convex. This conjecture concerns existence and uniqueness fo…

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…