# Jenkins-Serrin problem for translating horizontal graphs in $M \times\mathbb{R}$

## TL;DR

This paper establishes the existence of translating soliton graphs solving the Jenkins-Serrin problem in product manifolds, providing explicit examples in Euclidean and hyperbolic settings.

## Contribution

It introduces the concept of Jenkins-Serrin graphs as translating solitons in Riemannian products, expanding the class of known solutions in geometric flow theory.

## Key findings

- Existence of Jenkins-Serrin translating graphs in $M imes
$
- Explicit examples in $
^3$ and $H^2 imes
$
- New solutions to mean curvature flow in product manifolds

## Abstract

We prove the existence of horizontal Jenkins-Serrin graphs that are translating solitons of the mean curvature flow in Riemannian product manifolds $M\times\mathbb{R}$. Moreover, we give examples of these graphs in the cases of $\mathbb{R}^3$ and $\mathbb{H}^2\times\mathbb{R}$.