  In a 2004 paper, Lindblad demonstrated that the minimal surface equation on
$\mathbb{R}l^{1,1}$ describing graphical time-like minimal surfaces embedded in
$\mathbb{R}^{1,2}$ enjoy small data global existence for compactly supported
initial data, using Christodoulou's conformal method. Here we give a different,
geometric proof of the same fact, which exposes more clearly the inherent null
structure of the equations, and which allows us to also close the argument
using relatively few derivatives and mild decay assumptions at infinity.
