Logarithmically convex domain

Summary

A logarithmically convex domain is a Reinhardt domain whose image under the map $z \mapsto (\log\abs{z_1}, \dots, \log\abs{z_n})$ is a convex subset of $\R^n$. The domain of convergence of a power series always has this property. For complete Reinhardt domains, logarithmic convexity is exactly the condition that the domain is a domain of holomorphy. The notion is close to that of a logarithmically convex function: a function is logarithmically convex when its logarithm is convex.