Curvature estimates for the level sets of solutions to the Monge-Ampère equation detD 2 u = 1

Chuanqiang Chen; Xinan Ma; Shujun Shi

doi:10.1007/s11401-014-0864-6

Chinese Annals of Mathematics, Series B ›› 2014, Vol. 35 ›› Issue (6) : 895 -906. DOI: 10.1007/s11401-014-0864-6

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Curvature estimates for the level sets of solutions to the Monge-Ampère equation detD ² u = 1

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Abstract

For the Monge-Ampère equation detD ² u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained.

Keywords

Curvature estimates / Level sets / Monge-Ampère equation

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Chuanqiang Chen, Xinan Ma, Shujun Shi. Curvature estimates for the level sets of solutions to the Monge-Ampère equation detD ² u = 1. Chinese Annals of Mathematics, Series B, 2014, 35(6): 895-906 DOI:10.1007/s11401-014-0864-6

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