# Translating solitons $C^1-$asymptotic to two half-hyperplanes

## TL;DR

This paper proves the uniqueness of certain translating solitons in ^{n+1} that are asymptotic to two half-hyperplanes, specifically hyperplanes parallel to a given direction, outside a vertical cylinder.

## Contribution

It establishes a uniqueness result for translating solitons with specific asymptotic behavior, expanding understanding of their geometric structure.

## Key findings

- Hyperplanes parallel to _{n+1} are the only translating solitons asymptotic to two half-hyperplanes outside a vertical cylinder.
- The result characterizes the geometric structure of such solitons in ^{n+1}.
- Provides a classification of translating solitons with given asymptotic conditions.

## Abstract

We prove that the hyperplanes parallel to ${\bf e}_{n+1}$ are the unique examples of translating solitons $C^1-$asymptotic to two half-hyperplanes outside a vertical cylinder in $\R^{n+1}$.