论文标题
具有边界奇异性
Complex geodesics and complex Monge-Ampère equations with boundary singularity
论文作者
论文摘要
我们在$ \ Mathbb c^n $中研究了有界强的凸面域上的复杂的测量学和复杂的monge-ampère方程。更具体地说，当它的边界是最小的规律性时，我们证明了具有规定的边界价值和方向的复杂大地测量学的独特性。第一作者在1990年代初证明了这种复杂的测量学的存在，但独特性是开放的。基于这里证明的存在和独特性以及其他先前获得的结果，我们以规定的边界奇异性解决了一个均匀的复杂Monge-ampère方程，Bracci等人首先考虑了这一点。在平滑界限上，在$ \ mathbb c^n $中的强烈凸域。
We study complex geodesics and complex Monge-Ampère equations on bounded strongly linearly convex domains in $\mathbb C^n$. More specifically, we prove the uniqueness of complex geodesics with prescribed boundary value and direction in such a domain, when its boundary is of minimal regularity. The existence of such complex geodesics was proved by the first author in the early 1990s, but the uniqueness was left open. Based on the existence and the uniqueness proved here, as well as other previously obtained results, we solve a homogeneous complex Monge-Ampère equation with prescribed boundary singularity, which was first considered by Bracci et al. on smoothly bounded strongly convex domains in $\mathbb C^n$.
