Hessian一型方程在穿孔平面上的解空间
The space of solutions to the Hessian one equation in the finitely punctured plane
摘要：
我们构造了椭圆型Monge-Ampere方程det（D^2 u）=1在平面R^2上去掉n个点后的解空间。我们证明了，模等仿射变换和n>1，这个空间可以被看作是一个开子集的R^{3 n-4}，其中的坐标描述的共形等价类的一次穿孔有界域的复平面的连通n-1。这种方法实际上提供了一个构造性的过程，恢复所有这样的解决方案的蒙格-安培方程，并推广了一个定理K。乔根斯
英文摘要：
We construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo equiaffine transformations and for n>1, this space can be seen as an open subset of R^{3n-4}, where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.
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