The H-flow translating solitons in R^3 and R^4

TL;DR

This paper constructs explicit solutions for translating solitons in Euclidean 3- and 4-space, advancing understanding of mean curvature flow and proposing a conjecture on their non-existence in certain cases.

Contribution

It provides explicit solutions to the Hoffman-Osserman Gauss map problem for non-minimal translators and introduces a conjecture on the non-existence of Jenkins-Serrin type graphical translators.

Findings

Explicit solutions to the Gauss map problem in R^4

A conjecture on the non-existence of certain translators

Insights into mean curvature flow in higher dimensions

Abstract

Motivated by Ilmanen's correspondence, we present an explicit solution to the prescribed Hoffman-Osserman Gauss map problem for non-minimal translators to the mean curvature flow in Euclidean 4-space. We propose a conjecture on the non-existence of Jenkins-Serrin type unit-speed graphical translators.