复环面的Suita猜想
Suita Conjecture for a Complex Torus
摘要：
证明了对任何复环面，广义Suita猜想成立，即$ απK \geq c^2(α\in\mathbb R)$，$c$是修正对数容量，$K$是对角线上的Bergman核.对亏格为$\geq2$的一般紧致Riemann曲面的公开问题也作了详细的阐述。证明部分依赖于椭圆函数理论。
英文摘要：
The author proves that the generalized Suita conjecture holds for any complex torus, which means that $ απK \geq c^2(α\in\mathbb R)$, $c$ being the modified logarithmic capacity and $K$ being the Bergman kernel on the diagonal. The open problems for general compact Riemann surfaces with genus $\geq2$ is also elaborated. The proof relies in part on elliptic function theories.
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