论文标题
伯格曼内核的最低点的刚性定理
Rigidity theorem by the minimal point of the Bergman kernel
论文作者
论文摘要
我们使用suta猜想（现在是一个定理）来证明，对于任何域$ω\ subset \ subset \ mathbb {c} $它的伯格曼内核$ k（\ cdot，\ cdot）$满足$ k（z_0，z_0，z_0，z_0）= \ hbox {polumial} $ ys $ z_____________________________ $ if $ in of in of in of in of in of磁盘减去A（可能为空）封闭极性集，或$ \ Mathbb {C} $减去A（可能为空的）封闭极性集。当$ω$与$ c^{\ infty} $边界界定时，我们使用零组SzegöKernel提供了简单的证明。最后，我们表明该定理无法通过构建一个有限的完整的Reinhardt域（带有代数边界）来固定在$ \ mathbb {C}^n $中，而该定理不符合$ n> 1 $，该域（具有代数边界）强烈凸出而不是biholomorphic，而不是对单位球$ \ mathb $ \ mathb {b}^n \ subset \ subset \ subset \ subset \ bb n $ biholomorphic。
We use the Suita conjecture (now a theorem) to prove that for any domain $Ω\subset \mathbb{C}$ its Bergman kernel $K(\cdot, \cdot)$ satisfies $K(z_0, z_0) = \hbox{Volume}(Ω)^{-1}$ for some $z_0 \in Ω$ if and only if $Ω$ is either a disk minus a (possibly empty) closed polar set or $\mathbb{C}$ minus a (possibly empty) closed polar set. When $Ω$ is bounded with $C^{\infty}$-boundary, we provide a simple proof of this using the zero set of the Szegö kernel. Finally, we show that this theorem fails to hold in $\mathbb{C}^n$ for $n > 1$ by constructing a bounded complete Reinhardt domain (with algebraic boundary) which is strongly convex and not biholomorphic to the unit ball $\mathbb{B}^n \subset \mathbb{C}^n$.
