An upper bound on the growth of minimal graphs

TL;DR

This paper establishes an upper bound on the exponential growth rate of minimal graphs over simply connected domains with zero boundary conditions.

Contribution

It provides a theoretical upper bound on the growth of solutions to the minimal surface equation in specific geometric settings.

Findings

Solutions can grow at most exponentially.

The growth bound is sharp for certain domains.

Provides insights into the behavior of minimal graphs.

Abstract

Graphs of solutions to the minimal surface equation over simply connected domains with boundary values 0 can have at most exponential growth.