Suita Conjecture for a Complex Torus

Abstract

The author proves that the generalized Suita conjecture holds for any complex torus, which means that $\alpha \pi K\ge c^2(\alpha \in \mathbb{R})$, $c$ being the modified logarithmic capacity and $K$ being the Bergman kernel on the diagonal. The open problems for general compact Riemann surfaces with genus $\ge 2$ is also elaborated. The proof relies in part on elliptic function theories.

arXiv comment6 pages, 3 figures