Curvature estimates for the level sets of solutions of the Monge-Amp\`ere equation D2 u=1
Abstract
For the Monge-Amp\`ere equation D2 u=1, we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estimates for the Gauss curvature and mean curvature of the level sets for the solution to this equation.
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