4 problems

Let $w$ be a Lipschitz subsolution to the generalized $k$-convexity equation for $\beta=1$. A measure-valued Hessian conjecture asserts that there exist signed Borel measures…

Higher-dimensional constant-data uniqueness conjecture. Then $h$ must be a constant solution.

The quadratic-form conjecture. For every $n4$-dimensional vector $\xi=(\xi_1,\ldots,\xi_n)\in\mathbb{R}^n4$, the quadratic form

Let $u^*$ be the convex, $C^{1,1}(\mathbb{R}^n)$ solution associated to the eigenvalue $\lambda^*$, and define … where the infimum is over the relevant $C^2(\mathbb{R}^n)$ supersol…