New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909665077493760 |
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| author | Wu, Jie |
| author_facet | Wu, Jie |
| contents | In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type inequalities for static convex hypersurfaces in hyperbolic space $\mathbb{H}^n$ and for convex hypersurfaces in the sphere $\mathbb{S}^n$. The tools we shall use are the locally constrained inverse curvature flows in hyperbolic space and in the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms Wu, Jie Differential Geometry In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type inequalities for static convex hypersurfaces in hyperbolic space $\mathbb{H}^n$ and for convex hypersurfaces in the sphere $\mathbb{S}^n$. The tools we shall use are the locally constrained inverse curvature flows in hyperbolic space and in the sphere. |
| title | New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.22877 |