Logarithmically convex set

A Reinhardt domain $D$ is called logarithmically convex if the image of the set ${\displaystyle D^{*}=\{z=(z_{1},\cdots ,z_{n})\in D/z_{1}\cdots z_{n}\neq 0\}}$ under the mapping ${\displaystyle \lambda :z\rightarrow \lambda (z)=(\ln(|z_{1}|),\cdots ,\ln(|z_{n}|))}$ is a convex set in the real space $\mathbb {R} ^{n}$.

References

• E.D. Solomentsev. "Reinhardt domain". Encyclopedia of Mathematics. Retrieved 22 February 2015.