Contraction of hypersurfaces with positive sectional curvature in hyperbolic space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915963081850880 |
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| author | Luo, Tianci Wei, Yong Zhou, Rong |
| author_facet | Luo, Tianci Wei, Yong Zhou, Rong |
| contents | We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space $\mathbb{H}^{n+1}$. The speed is assumed to be homogeneous of degree one in the principal curvatures and to satisfy certain conditions. This class of flows includes the $k$th mean curvature flow as a special case. We show that if the initial hypersurface has positive sectional curvature, then this property is preserved along the flow, and the evolving hypersurface contracts to a round point in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contraction of hypersurfaces with positive sectional curvature in hyperbolic space Luo, Tianci Wei, Yong Zhou, Rong Differential Geometry We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space $\mathbb{H}^{n+1}$. The speed is assumed to be homogeneous of degree one in the principal curvatures and to satisfy certain conditions. This class of flows includes the $k$th mean curvature flow as a special case. We show that if the initial hypersurface has positive sectional curvature, then this property is preserved along the flow, and the evolving hypersurface contracts to a round point in finite time. |
| title | Contraction of hypersurfaces with positive sectional curvature in hyperbolic space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.25513 |