摘要
For the Monge-Amp`ere equation det D2u = 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.
For the Monge-Ampere equation det D2u = 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.
基金
supported by the Chinese Universities Scientific Fund(No.WK0010000028)
supported by the National Science Fund for Distinguished Young Scholars of China and Wu Wen-Tsun Key Laboratory of Mathematics
partially supported by the National Natural Science Foundation of China(Nos.11101110,11326144)
the Foundation of Harbin Normal University(No.KGB201224)
