A Sharp Bound for the Growth of Minimal Graphs

TL;DR

This paper establishes precise bounds for solutions to the minimal surface equation in domains with sector-shaped boundaries larger than pi, advancing understanding of minimal graph growth.

Contribution

It provides sharp bounds for minimal graphs over sectors with opening angles greater than pi, improving previous estimates.

Findings

Derived exact bounds for minimal surface solutions

Extended bounds to sectors with large opening angles

Enhanced theoretical understanding of minimal graph behavior

Abstract

Sharp bounds are given for solutions to the minimal surface equation with vanishing boundary values over domains containing sectors of opening bigger than pi.