Solution
= Solution
Curves $\alpha_1,\ldots,\alpha_n$ in minimal position <fill a surface> $S$ when every essential simple closed curve has positive geometric intersection with at least one $\alpha_i$. On a closed surface this is equivalent to every component of
$$
S\setminus\bigcup_i\alpha_i
$$
being a disc: a non-disc complementary component contains an essential curve, while any curve disjoint from the collection lies in such a component.