Boundary behavior of a conformal mapping
John N. Marafino · Pacific Journal of Mathematics · 1992
Let D be a simply connected plane domain, not the whole plane.Let R* denote those accessible boundary points of D such that D twists violently about them; that is, if a G R* and w(a) denotes its complex coordinate, then lim inf arg(ww(a)) = -oo and lim suparg(ww(a)) = +oo, tυeS where arg(w -w(a)) is defined and continuous in D. We show that if a certain geometric condition holds at each point of a set W* c R*, then W* is a Z)-conformal null set.Let L v denote the ray with terminal point w(a), a € R* , having inclination v, 0 '< 3, and M(I/, ) < 1 for / = 1,2,3}.THEOREM.W* is a D-conformal null set.