8 papers
Remarks on the disjoint minimal graphs conjecture
Allen Weitsman
It is known that there can be at most 3 disjoint nontrivial minimal graphs in R^3 with 0 boundary values, and conjectured that there can be at most 2. We explore properties that th…
An upper bound on the growth of minimal graphs
Allen Weitsman
Graphs of solutions to the minimal surface equation over simply connected domains with boundary values 0 can have at most exponential growth.
Univalent approximation by Fourier series of step functions
Allen Weitsman
We prove that univalent harmonic mappings can be approximated by univalent Fourier series of step functions.
A lower bound on the growth of minimal graphs
Allen Weitsman
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.
Level Curves of Minimal Graphs
Allen Weitsman
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 conc…
A Sharp Bound for the Growth of Minimal Graphs
Allen Weitsman
Sharp bounds are given for solutions to the minimal surface equation with vanishing boundary values over domains containing sectors of opening bigger than pi.