Measurements of Riemannian two-disks and two-spheres
We prove that any Riemannian two-sphere having area at most 1 can be continuously mapped onto a tree in such a way that the topology of the fibers is controlled and their length is less than 7.6. This result improves previous estimates and relies on a similar statement for Riemannian two-disks.
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:287686 |
| Online Access: | https://ddd.uab.cat/record/287686 https://dx.doi.org/urn:doi:10.2140/pjm.2015.275.167 |
| Access Level: | Open access |
| Keyword: | Bers constant Closed geodesic Curvature-free inequalities Isoperimetric inequalities Width |
| Summary: | We prove that any Riemannian two-sphere having area at most 1 can be continuously mapped onto a tree in such a way that the topology of the fibers is controlled and their length is less than 7.6. This result improves previous estimates and relies on a similar statement for Riemannian two-disks. |
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