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where Tu = Du √ 1 + |Du|2 and Du = (ux, uy). In 1965, Nitsche [5] announced the following result: “Let Ωα ⊂ R be a sector with angle 0 < α < π. If u satisfies the minimal surface equation with vanishing boundary value in Ωα, then u ≡ 0”. Hwang extends this result in [3], [4] and proves that, in an unbounded domain Ω properly contained in the half plane in R, if u satisfies the minimal surface equation, then, the growth property of u is determined completely by the shape of Ω and the boundary value of u. In this respect, the Phragmen-Lindelof theorem for the minimal surface equation is better than that for the Laplace equation; (indeed, if u satisfies the Laplace equation in an unbounded domain Ω, the growth property of u cannot be determined completely by the shape of Ω and the boundary data of u alone [8]). One of the results in [4] is the following:

Catenoid-like solutions for the minimal surface equation