Abstract:The curvature of the level set of elliptic partial differential equation solutions is always an important content in the study of convexity. Curvature is an important invariant of surface, which characterizes the degree of curve bending, is the important basis of differential geometry. Curvature is widely used in machining. In this paper, we study the completely nonlinear elliptic Monge-Ampère equation 2 det u D u e = with 0 boundary value Dirichlet condition in four-dimensional Euclidean space. It is proved t… Show more
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