Logarithmically convex set

A Reinhardt domain D is called logarithmically convex if the image of the set D ∗ = { z = ( z 1 , ⋯ , z n ) ∈ D / z 1 ⋯ z n ≠ 0 } under the mapping λ : z → λ ( z ) = ( ln ⁡ ( | z 1 | ) , ⋯ , ln ⁡ ( | z n | ) ) is a convex set in the real space R n .