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arXiv · 1305.2669

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

Chuanqiang Chen·Xi-Nan Ma·Shujun Shi
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Abstract

For the Monge-Amp\`{e}re 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 estimates for the Gauss curvature and mean curvature of the level sets for the solution to this equation.

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Chuanqiang Chen, Xi-Nan Ma, Shujun Shi. 2013-05-13. Curvature estimates for the level sets of solutions of the Monge-Amp\`{e}re equation $\det D^2 u=1$. https://arxiv.org/abs/1305.2669

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