On the growth of minimal graphs

Abstract. We consider minimal graphs u = u(x; y)> 0 over unbounded domains D R2 with @D a piecewise smooth curve on which u = 0. We give some lower growth estimates for u in terms of the geometry of D. I. Introduction. Let D be an unbounded domain in R2 bounded by a piecewise dierentiable arc, and 0 (r) 2 be the angular measure of the set D \ fjzj = rg. In the classical potential theory of harmonic functions, an important role is played by estimates involving (r). For example, if u(z) is the harmonic measure of D \ fjzj < rg with respect to D \ fjzj = rg, then [T; p.116] we hav