On the geometry of the asymptotic boundary of translators in $\mathbb H^2\times \mathbb R$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909625065930752 |
|---|---|
| author | Pipoli, Giuseppe Santos, Joao Paulo dos Tinaglia, Giuseppe |
| author_facet | Pipoli, Giuseppe Santos, Joao Paulo dos Tinaglia, Giuseppe |
| contents | In this work, we study complete properly immersed translators in the product space $\mathbb H^2\times\mathbb R$, focusing on their asymptotic behavior at infinity. We classify the asymptotic boundary components of these translators under suitable continuity assumptions. Specifically, we prove that if a boundary component lies in the vertical asymptotic boundary, it is of the form $\{p\}\times [T,\infty)$ or $\{p\}\times \mathbb R$, while if it lies in the horizontal asymptotic boundary, it is a complete geodesic. Our approach is inspired by earlier work on minimal and constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$, with a key ingredient being the use of symmetric translators as barriers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometry of the asymptotic boundary of translators in $\mathbb H^2\times \mathbb R$ Pipoli, Giuseppe Santos, Joao Paulo dos Tinaglia, Giuseppe Differential Geometry 53A10, 53C42, 53C44 In this work, we study complete properly immersed translators in the product space $\mathbb H^2\times\mathbb R$, focusing on their asymptotic behavior at infinity. We classify the asymptotic boundary components of these translators under suitable continuity assumptions. Specifically, we prove that if a boundary component lies in the vertical asymptotic boundary, it is of the form $\{p\}\times [T,\infty)$ or $\{p\}\times \mathbb R$, while if it lies in the horizontal asymptotic boundary, it is a complete geodesic. Our approach is inspired by earlier work on minimal and constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$, with a key ingredient being the use of symmetric translators as barriers. |
| title | On the geometry of the asymptotic boundary of translators in $\mathbb H^2\times \mathbb R$ |
| topic | Differential Geometry 53A10, 53C42, 53C44 |
| url | https://arxiv.org/abs/2505.21083 |