Biholomorphisms between Hartogs domains over homogeneous Siegel domains

全纯函数在对称塞格尔域上的不变空间

Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains

本文研究了对称塞格尔域上的全纯函数的不变空间，通过分类仿射不变半希尔伯特空间并改进莫比乌斯不变半希尔伯特空间的分类，揭示了其在一般域上的结构。

A Kähler potential on the unit ball with constant differential norm

Let $\mathbb B^n$ be the unit ball in $\mathbb C^n$ and $\mathbb H^n$ be the homogeneous Siegel domain of the second kind which is biholomorphic to $\mathbb B^n$. We show that the Kähler potential of $\mathbb H^n$ is unique up to the automorphisms among Kähler potentials whose differentials have constant norms. As an application, we consider a domain $Ω$ in $\mathbb C^n$, which is biholomorphic to $\mathbb B^n$. We show that if $Ω$ is affine homogeneous, then it is affine equivalent to $\mathbb H^n$. Assume next that its canonical potential with respect to the Kähler--Einstein metric has a dif…