Solution
= Solution
Since $V$ is simply connected, $g$ has a primitive $G_0$. On connected $U\cap V$, $G_0-F$ has zero <derivative> and is constant. Adjust that constant to obtain $G=F$ on the overlap, hence the required continuation.
= Solution
Since $V$ is simply connected, $g$ has a primitive $G_0$. On connected $U\cap V$, $G_0-F$ has zero <derivative> and is constant. Adjust that constant to obtain $G=F$ on the overlap, hence the required continuation.