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arXiv · 1401.7184

Measurements of Riemannian two-disks and two-spheres

Florent Balacheff
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Abstract

We prove that any Riemannian two-sphere with area at most 1 can be continuously mapped onto a tree in a such a way that the topology of 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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Florent Balacheff. 2014-01-28. Measurements of Riemannian two-disks and two-spheres. https://doi.org/10.2140/pjm.2015.275.167

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