Abstract: | Suppose that C1 and C2 are two simple curves joining 0 to ,non-intersecting in the finite plane except at 0 and enclosinga domain D which is such that, for all large r, has measure at most 2, where 0 < < .Suppose also that u is a non-constant subharmonic function inthe plane such that u(z) = B(|z|, u) for all large z C1 C2.Let AD(r, u) = inf { u(z):z D and | z | = r }. It is shownthat if AD(r, u) = O(1) (or AD(r, u) = o(B(r, u))), then limr B(r, u)/r/2 > 0 (or limr log B(r, u)/log r /2). |