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| Curvature Estimates for the Level Sets of Solutions to theMonge-Amp`ere Equation detD2u = 1 |
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Citation： |
Chuanqiang CHEN,Xinan MA,Shujun SHI.Curvature Estimates for the Level Sets of Solutions to theMonge-Amp`ere Equation detD2u = 1[J].Chinese Annals of Mathematics B,2014,35(6):895~906 |
| Page view： 1485
Net amount： 1280 |
Authors： |
Chuanqiang CHEN; Xinan MA; Shujun SHI; |
Foundation： |
the Chinese Universities Scientific Fund (No.WK0010000028). The
second author was supported by the National Science Fund for Distinguished Young Scholars of China
and Wu Wen-Tsun Key Laboratory of Mathematics. The third author was partially supported by the
National Natural Science Foundation of China (Nos. 11101110, 11326144) and the Foundation of Harbin
Normal University (No.KGB201224). |
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| Abstract： |
For the Monge-Ampere equation detD2u = 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-Amp`ere equation |
Classification： |
35J65 |
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