Measurements of Riemannian two-disks and two-spheres

Florent Balacheff*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)167-181
Number of pages15
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 2015


  • Bers constant
  • Closed geodesic
  • Curvature-free inequalities
  • Isoperimetric inequalities
  • Width


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