Curvature estimates for the level sets of solutions of the Monge-Ampère equation $\det D^{2}u=1$

Chuanqiang Chen, Xi-Nan Ma, Shujun Shi

For the Monge-Ampère equation $\det D^{2}u=1$, we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estim…