二维黎曼流形上蒙日-安培方程解的一个估计

An Estimate of the Solution of the Monge- Ampère Equation in 2- dimensional Riemannian Manifolds

主要介绍在二维常曲率黎曼流形中,对于蒙日-安培方程det D2u=1的Dirichlet问题,给出与解有关的一个辅助函数φ在边界达到最大值.

In this paper, in the 2 - dimensional Riemannian Manifolds, the Dirichlet problem of Monge- Ampere equation det D：u = 1 is introduced, a auxilary function φ which is related to the solution is foundand its maximum on the boundary is got.