Starshaped compact hypersurfaces in warped product manifolds II: a class of Hessian type equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910615508877312 |
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| author | Wang, Bin |
| author_facet | Wang, Bin |
| contents | In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed Weingarten curvature. J. Geom. Anal. $\textbf{34}$ (2024).] from the Euclidean space to Riemannian warped products. Moreover, we show that interior second order a priori estimates for admissible solutions to the associated fully nonlinear elliptic partial differential equations can be readily established by similar arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Starshaped compact hypersurfaces in warped product manifolds II: a class of Hessian type equations Wang, Bin Differential Geometry Analysis of PDEs Primary 53C21, Secondary 35J60 In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed Weingarten curvature. J. Geom. Anal. $\textbf{34}$ (2024).] from the Euclidean space to Riemannian warped products. Moreover, we show that interior second order a priori estimates for admissible solutions to the associated fully nonlinear elliptic partial differential equations can be readily established by similar arguments. |
| title | Starshaped compact hypersurfaces in warped product manifolds II: a class of Hessian type equations |
| topic | Differential Geometry Analysis of PDEs Primary 53C21, Secondary 35J60 |
| url | https://arxiv.org/abs/2405.04882 |