Let $\mathbb{C}^n$ be the complex Euclidean space. The wiki of contractible tells us that any Euclidean space is contractible, as is any star domain on a Euclidean space.
My question is:
1, Is a Euclidean convex domain in $\mathbb{C}^n$ contractible? (An Euclidean convex domain seems to be a star domain)
2, Is a domain of holomorphy (which is weaker than Euclidean convex) in $\mathbb{C}^n$ contractible?
3, Is a simply connected open subset of $\mathbb{C}^n$ contractible?
Thanks a lot.