A prescribed curvature flow on hyperbolic surfaces with infinite topological type
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918034921226240 |
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| author | Zhao, Xinrong Zhou, Puchun |
| author_facet | Zhao, Xinrong Zhou, Puchun |
| contents | In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce a prescribed curvature flow-a discrete analogue of the Ricci flow on noncompact surfaces-specifically adapted to the setting of infinite cellular decompositions. We establish the well-posedness of the flow and prove two convergence results under certain conditions. Our approach resolves the prescribed total geodesic curvature problem for a broad class of surfaces with infinite cellular decompositions, yielding, in certain cases, smooth hyperbolic surfaces of infinite topological type with geodesic boundaries or cusps. Moreover, the proposed flow provides a method for constructing hyperbolic metrics from appropriate initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A prescribed curvature flow on hyperbolic surfaces with infinite topological type Zhao, Xinrong Zhou, Puchun Geometric Topology Differential Geometry 52C26, 51M10, 57M50 In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce a prescribed curvature flow-a discrete analogue of the Ricci flow on noncompact surfaces-specifically adapted to the setting of infinite cellular decompositions. We establish the well-posedness of the flow and prove two convergence results under certain conditions. Our approach resolves the prescribed total geodesic curvature problem for a broad class of surfaces with infinite cellular decompositions, yielding, in certain cases, smooth hyperbolic surfaces of infinite topological type with geodesic boundaries or cusps. Moreover, the proposed flow provides a method for constructing hyperbolic metrics from appropriate initial data. |
| title | A prescribed curvature flow on hyperbolic surfaces with infinite topological type |
| topic | Geometric Topology Differential Geometry 52C26, 51M10, 57M50 |
| url | https://arxiv.org/abs/2505.20091 |