Convex Hull Volumes in Hyperbolic 3-Space
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909016034115584 |
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| author | MacMahon, Cameron |
| author_facet | MacMahon, Cameron |
| contents | In this paper we provide a geometric condition satisfied by certain closed subsets of the Riemann sphere which implies that their hyperbolic convex hulls in $\mathbb{H}^3$ have infinite volume. As a corollary, we characterize continua in the Riemann sphere whose hyperbolic convex hulls have infinite volume, answering a question of Danny Calegari. Furthermore, we give a geometric characterization of planar self-similar sets whose hyperbolic convex hulls have infinite volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex Hull Volumes in Hyperbolic 3-Space MacMahon, Cameron Geometric Topology Metric Geometry In this paper we provide a geometric condition satisfied by certain closed subsets of the Riemann sphere which implies that their hyperbolic convex hulls in $\mathbb{H}^3$ have infinite volume. As a corollary, we characterize continua in the Riemann sphere whose hyperbolic convex hulls have infinite volume, answering a question of Danny Calegari. Furthermore, we give a geometric characterization of planar self-similar sets whose hyperbolic convex hulls have infinite volume. |
| title | Convex Hull Volumes in Hyperbolic 3-Space |
| topic | Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2604.27291 |