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math.AP2013
On the growth of solutions to the minimal surface equation over domains containing a halfplane
Erik Lundberg, Allen Weitsman
We consider minimal graphs u(x,y)>0 over unbounded domains D (with u vanishing on the boundary of D). Assuming D contains a sector properly containing a halfplane, we obtain estima…
math.CV2013
A solution to Sheil-Small's harmonic mapping problem for Jordan polygons
Daoud Bshouty, Erik Lundberg, Allen Weitsman
The problem of mapping the interior of a Jordan polygon univalently by the Poisson integral of a step function was posed by T. Sheil-Small (1989). We describe a simple solution usi…