State the Uniformization Theorem.

Show that any domain of $\mathbb{C}$ whose complement has more than one point is uniformized by the unit disc $\Delta .$ [You may use the fact that for $\mathbb{C}_{\infty}$ the group of automorphisms consists of Möbius transformations, and for $\mathbb{C}$ it consists of maps of the form $z \mapsto a z+b$ with $a \in \mathbb{C}^{*}$ and $b \in \mathbb{C}$.

Let $X$ be the torus $\mathbb{C} / \Lambda$, where $\Lambda$ is a lattice. Given $p \in X$, show that $X \backslash\{p\}$ is uniformized by the unit $\operatorname{disc} \Delta$.

Is it true that a holomorphic map from $\mathbb{C}$ to a compact Riemann surface of genus two must be constant? Justify your answer.