A remark on a Bernstein type theorem for entire Willmore graphs in R^3

TL;DR

This paper proves that entire Willmore graphs in three-dimensional space with finite mean curvature are necessarily planes, extending understanding of geometric properties of such surfaces.

Contribution

It establishes a Bernstein-type theorem for entire Willmore graphs with square integrable mean curvature in R^3.

Findings

Every entire Willmore graph in R^3 with square integrable mean curvature is a plane.

The result generalizes classical Bernstein theorems to Willmore surfaces.

Provides a new characterization of minimality for certain classes of surfaces.

Abstract

In this note we prove that every two-dimensional entire Willmore graph in $R^3$ with square integrable mean curvature is a plane.