Logarithmically convex set

A Reinhardt domain $D$ is called logarithmically convex if the image of the set $D^* = \{z=(z_1, \cdots, z_n) \in D / z_1 \cdots z_n \neq 0\}$ under the mapping $\lambda : z \rightarrow \lambda(z) = (\ln(|z_1|), \cdots, \ln(|z_n|))$ is a convex set in the real space $\mathbb{R}^n$ .