Theorem 1.1 . [04TK]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Theorem 1.1.

Assume $u$ is an Alexandrov solution to

\det D^{2}u\geq 1

in $B_{1}\subset\mathbb{R}^{n}$ . Then $u$ is strictly convex away from a singular set $\Sigma$ with

\mathcal{H}^{n-1}(\Sigma)=0.