Graphical Translators for Mean Curvature Flow

TL;DR

This paper classifies all complete translating graphs in three-dimensional space and introduces new families of translating graphs in higher dimensions, advancing understanding of mean curvature flow.

Contribution

It provides a complete classification in 3D and constructs new multi-parameter families of translating graphs in higher dimensions.

Findings

Complete classification of translating graphs in R^3.

Construction of two new families of translating graphs in R^{n+1}.

Advancement in the understanding of mean curvature flow.

Abstract

In this paper we provide a full classification of complete translating graphs in $\mathbf{R}^3$. We also construct two $(n-1)$-parameter families of new examples of translating graphs in $\mathbf{R}^{n+1}$.