what is $\mathbb{D}^{-}$? Clarification of notation

Question

I am reading an article here. I came across the notation $\mathbb{D}^{-}$, started from proposition 4.1(p.11 of the pdf). I understand that $\mathbb{D}$ is the set $\{z\in\mathbb{C},|z|<1\}$, which is already explained in the article. However I can't find the definition of $\mathbb{D}^{-}$, so I would like to know its meaning, especially if $\mathbb{D}^{-}$ contain 0 or not.