A reverse Denjoy theorem
Peter C. Fenton, John Rossi · Bulletin of the London Mathematical Society · 2008
Suppose that C1 and C2 are two simple curves joining 0 to ∞, non-intersecting in the finite plane except at 0 and enclosing a domain D which is such that, for all large r, { θ : r e i θ ∈ D ¯ } has measure at most 2α, where 0 0 (or limr→∞ log B(r, u)/log r ⩾ π/2α).