| 董欣.复环面情形的Suita猜想[J].数学年刊A辑,2014,35(1):101~108 |
| 复环面情形的Suita猜想 |
| Suita Conjecture for a Complex Torus |
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| DOI： |
| 中文关键词: Suita猜想, 复环面, Bergman核, Arakelov-Green函数 |
| 英文关键词:Suita conjecture, Complex torus, Bergman kernel, Arakelov-Green's function |
| 基金项目:国家自然科学基金 (No.11031008, No.11171255)和名古屋大学2012年学生项目 |
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| 中文摘要: |
| 对任意复环面的情形证明了推广的Suita猜想, 即$ \alpha\pi K \geq c^2\ (\alpha \in \mathbb R)$,
其中$c$ 是修正后的对数容度, $K$是对角线上的Bergman 核. 还阐明了对任意亏格$\geq2$的紧Riemann面情形的公开问题.
文中结果的证明部分地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
$\alpha\pi K \geq c^2\ (\alpha\in\mathbb R)$, $c$ being the modified logarithmic capacity, and $K$
being the Bergman kernel on the diagonal. The open problem for general compact
Riemann surfaces with genus $\geq2$ is also elaborated. The proof relies in part on elliptic function theories. |
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