# Notes on translating solitons for Mean Curvature Flow

## TL;DR

This paper provides a comprehensive classification of complete translating graph solutions in three-dimensional space for the mean curvature flow, aiding understanding of their structure and properties.

## Contribution

It offers a complete classification of complete translating graphs in 3, advancing the understanding of translating solitons in mean curvature flow.

## Key findings

- Classification of all complete translating graphs in 3
- Description of properties of these solitons
- Insights into their geometric structure

## Abstract

The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$. In this paper we describe a full classification of complete translating graphs in $\mathbb{R}^3$.