An upper bound on the growth of minimal graphs
Graphs of solutions to the minimal surface equation over simply connected domains with boundary values 0 can have at most exponential growth.
math.DG↗
arXiv subjects
Allen Weitsman
Publications and source records attributed to Allen Weitsman.
Univalent approximation by Fourier series of step functions
We prove that univalent harmonic mappings can be approximated by univalent Fourier series of step functions.
math.CV↗
A lower bound on the growth of minimal graphs
We give the lower bound for the growth of the maximum value for a solution to the minimal surface equation with 0 boundary values over an unbounded simply connected domain.
math.DG↗
A Sharp Bound for the Growth of Minimal Graphs
Sharp bounds are given for solutions to the minimal surface equation with vanishing boundary values over domains containing sectors of opening bigger than pi.
math.DG↗
Level Curves of Minimal Graphs
We prove an inequality for the curvature of level sets of minimal graphs having vanishing boundary values and show that if the boundary is concave, then all the level sets are concave.
math.DG↗
On the growth of solutions to the minimal surface equation over domains containing a halfplane
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 estimates on growth and provide examples illustrating a range of growth.
math.AP↗
A solution to Sheil-Small's harmonic mapping problem for Jordan polygons
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 using "ear clipping" from computational geometry.
math.CV↗