$k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909194812129280 |
|---|---|
| author | Chen, Xiaojuan Tu, Qiang Xiang, Ni |
| author_facet | Chen, Xiaojuan Tu, Qiang Xiang, Ni |
| contents | In this paper, we consider Weingarten curvature equations for $k$-convex hypersurfaces with $n<2k$ in a warped product manifold $\overline{M}=I\times_λM$. Based on the conjecture proposed by Ren-Wang in \cite{Ren2}, which is valid for $k\geq n-2$, we derive curvature estimates for equation $σ_k(κ)= ψ(V, ν(V))$ through a straightforward proof. Furthermore, we also obtain an existence result for the star-shaped compact hypersurface $Σ$ satisfying the above equation by the degree theory under some sufficient conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds Chen, Xiaojuan Tu, Qiang Xiang, Ni Analysis of PDEs 53C45, 35J60 In this paper, we consider Weingarten curvature equations for $k$-convex hypersurfaces with $n<2k$ in a warped product manifold $\overline{M}=I\times_λM$. Based on the conjecture proposed by Ren-Wang in \cite{Ren2}, which is valid for $k\geq n-2$, we derive curvature estimates for equation $σ_k(κ)= ψ(V, ν(V))$ through a straightforward proof. Furthermore, we also obtain an existence result for the star-shaped compact hypersurface $Σ$ satisfying the above equation by the degree theory under some sufficient conditions. |
| title | $k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds |
| topic | Analysis of PDEs 53C45, 35J60 |
| url | https://arxiv.org/abs/2405.03407 |