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arXiv · 1403.7447

Suita Conjecture for a Complex Torus

Robert Xin Dong
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Abstract

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 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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Robert Xin Dong. 2014-03-28. Suita Conjecture for a Complex Torus. https://doi.org/10.3103/s0898511114030077

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