Conformal solitons for the mean curvature flow in hyperbolic space
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910646874931200 |
|---|---|
| author | Mari, Luciano de Oliveira, Jose Danuso Rocha Savas-Halilaj, Andreas de Sena, Renivaldo Sodre |
| author_facet | Mari, Luciano de Oliveira, Jose Danuso Rocha Savas-Halilaj, Andreas de Sena, Renivaldo Sodre |
| contents | In this paper we study conformal solitons for the mean curvature flow in hyperbolic space $\mathbb{H}^{n+1}$. Working in the upper half-space model, we focus on horo-expanders, which relate to the conformal field $-\partial_0$. We classify cylindrical and rotationally symmetric examples, finding appropriate analogues of grim-reaper cylinders, bowl and winglike solitons. Moreover, we address the Plateau and the Dirichlet problems at infinity. For the latter, we provide the sharp boundary convexity condition to guarantee its solvability, and address the case of noncompact boundaries contained between two parallel hyperplanes of $\partial_{\infty}\mathbb{H}^{n+1}$. We conclude by proving rigidity results for bowl and grim-reaper cylinders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05088 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal solitons for the mean curvature flow in hyperbolic space Mari, Luciano de Oliveira, Jose Danuso Rocha Savas-Halilaj, Andreas de Sena, Renivaldo Sodre Differential Geometry Analysis of PDEs In this paper we study conformal solitons for the mean curvature flow in hyperbolic space $\mathbb{H}^{n+1}$. Working in the upper half-space model, we focus on horo-expanders, which relate to the conformal field $-\partial_0$. We classify cylindrical and rotationally symmetric examples, finding appropriate analogues of grim-reaper cylinders, bowl and winglike solitons. Moreover, we address the Plateau and the Dirichlet problems at infinity. For the latter, we provide the sharp boundary convexity condition to guarantee its solvability, and address the case of noncompact boundaries contained between two parallel hyperplanes of $\partial_{\infty}\mathbb{H}^{n+1}$. We conclude by proving rigidity results for bowl and grim-reaper cylinders. |
| title | Conformal solitons for the mean curvature flow in hyperbolic space |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2307.05088 |