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 $\mathbb {R} ^{n}$ .