Sharp Hausdorff Bounds for the Interior Singular Set of Convex $k$-Hessian Solutions

Xiyu Hu

Let $2\le k\le n$, let $\hat{I}\text{c◯}\subset {\mathbb{R}}^n$ be open and convex, and let $u$ be a convex viscosity solution of $\ddot{I}{ƒ}_k(D^{2}u)=1$ in $\hat{I}\text{c◯}$. We prove that the set on which $u$ fails to…