调和Bergman核诱导的距离与Riemann度量

Distances and Riemann Metrics Induced by Harmonic Bergman Kernels

利用Rn 中的有界域D的调和Bergman核,在Rn 中的有界域D上建立距离ρD 并利用ρD 在Rn 中的有界域D上建立Riemann度量.我们给出ρD 与Riemann度量的关系,证明如果有界域D关于ρD 完备。

We constructed the distance ρ D on the bounded domain D of R n,drawing on the harmonic Bergman kernel on D and constructed the Riemann metric on D,making use of ρ D.We gained the connection between ρ D and the Riemann metric on D;proved that if(D,ρ D)is complete,then the Riemann metric is complete.