Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establ...Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C^2 estimates and the existence theorem by the method of continuity.展开更多
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 th...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.展开更多
基金supported by ZJNSF No. LY17A010022NSFC No.11771396+2 种基金supported by NSFC No. 11471188Wu Wen-Tsun Key Laboratory of Mathematics in USTCsupported by China Scholarship Council
文摘Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C^2 estimates and the existence theorem by the method of continuity.
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+1 种基金partially supported by the National Natural Science Foundation of China(Nos.11101110,11326144)the Foundation of Harbin Normal University(No.KGB201224)
文摘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.
