that $$\sum_{j=1}^nf_jg_j=1?$$ We call the functions $\{f_j\}$ corona data, and the functions $\{g_j\}$ corona solutions. It has been conjectured that this can be answered in the affirmative for any planar domain. In the case of Riemann surfaces, a counterexample was first found by Brian Cole (see [@cole]), other examples being found later by D. E. Barrett and J. Diller [@barrett-diller], however, this is due to a structure that in some sense makes the surface seem higher dimensional, so one might hope that the restriction to the Riemann sphere might prevent this obstacle.

This problem was first posed in the case of the unit disc $\mathbb D$ by S. Kakutani in 1941, which case was solved by L. Carleson [@car-disc] in 1962. It is from this origin that the problem gets its name, as there would have been a set of maximal ideals suggestive of the sun’s corona has the theorem failed in this case. The proof was subsequently simplified by L. Hörmander [@hormander] by use of a $\bar\partial$-problem, and then later in an acclaimed proof by T. Wolff (see [@gamelin2] or [@garnett-baf]). A quite different proof of this result using techniques from several complex variables was later developed by B. 