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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.18974 |
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Table of Contents:
- In this paper we prove existence and classification results for translating solitons defined as initial conditions for higher order mean curvature flows that are invariant by translations in warped product manifolds $\mathbb{P}\times_χ\mathbb{R}$. Here, $\mathbb P$ is a Cartan-Hadamard manifold endowed with a rotationally symmetric metric and $χ$ is a radial function defined in $\mathbb{P}$. In this setting, the higher order mean curvature flow is, up to a change of time parameter, given by translations along the factor $\mathbb{R}$ in the warped product. This setting encompasses the cases of translating solitons in $\mathbb{R}^{n+1}$, $\mathbb{H}^n \times \mathbb{R}$ and $\mathbb{H}^{n+1}$ studied in recent papers. In particular we prove the existence of families of bowl-type and catenoid-type translating solitons under mild assumptions about the curvature of the warped product. We also describe the asymptotic behavior for those solitons in terms of the geometry at infinity of $\mathbb{P}$. Our assumptions about the ambient metric allow us to control the higher order mean curvature of cylinders and to use them as barriers.