The Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911762811453440 |
|---|---|
| author | Gomez, Michael Vieira, Matheus |
| author_facet | Gomez, Michael Vieira, Matheus |
| contents | In this paper we study the Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space. We show that if the image of the Gauss map is in a closed hemisphere, then the hypersurface is a hyperplane or a generalized cylinder. We also show that if the image of the Gauss map is in $S^{n}\setminus\bar{S}_{+}^{n-1}$, then the hypersurface is a hyperplane. This generalizes previous results for self-shrinkers obtained by Ding-Xin-Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00970 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space Gomez, Michael Vieira, Matheus Differential Geometry In this paper we study the Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space. We show that if the image of the Gauss map is in a closed hemisphere, then the hypersurface is a hyperplane or a generalized cylinder. We also show that if the image of the Gauss map is in $S^{n}\setminus\bar{S}_{+}^{n-1}$, then the hypersurface is a hyperplane. This generalizes previous results for self-shrinkers obtained by Ding-Xin-Yang. |
| title | The Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2312.00970 |