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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.03505 |
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| _version_ | 1866910765227704320 |
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| author | Bowers, Philip L. Ruffoni, Lorenzo |
| author_facet | Bowers, Philip L. Ruffoni, Lorenzo |
| contents | We show that given an infinite triangulation $K$ of a surface with punctures (i.e., with no vertices at the punctures) and a set of target cone angles smaller than $π$ at the punctures that satisfy a Gauss-Bonnet inequality, there exists a hyperbolic metric that has the prescribed angles and supports a circle packing in the combinatorics of $K$. Moreover, if $K$ is very symmetric, then we can identify the underlying Riemann surface and show that it does not depend on the angles. In particular, this provides examples of a triangulation $K$ and a conformal class $X$ such that there are infinitely many conical hyperbolic structures in the conformal class $X$ with a circle packing in the combinatorics of $K$. This is in sharp contrast with a conjecture of Kojima-Mizushima-Tan in the closed case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03505 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinite circle packings on surfaces with conical singularities Bowers, Philip L. Ruffoni, Lorenzo Geometric Topology Combinatorics 52C26, 30F60 We show that given an infinite triangulation $K$ of a surface with punctures (i.e., with no vertices at the punctures) and a set of target cone angles smaller than $π$ at the punctures that satisfy a Gauss-Bonnet inequality, there exists a hyperbolic metric that has the prescribed angles and supports a circle packing in the combinatorics of $K$. Moreover, if $K$ is very symmetric, then we can identify the underlying Riemann surface and show that it does not depend on the angles. In particular, this provides examples of a triangulation $K$ and a conformal class $X$ such that there are infinitely many conical hyperbolic structures in the conformal class $X$ with a circle packing in the combinatorics of $K$. This is in sharp contrast with a conjecture of Kojima-Mizushima-Tan in the closed case. |
| title | Infinite circle packings on surfaces with conical singularities |
| topic | Geometric Topology Combinatorics 52C26, 30F60 |
| url | https://arxiv.org/abs/2305.03505 |