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

Xiyu Hu

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