Measurements of Riemannian two-disks and two-spheres

Florent Balacheff

doi:10.2140/pjm.2015.275.167

Measurements of Riemannian two-disks and two-spheres

Florent Balacheff^*

^*Corresponding author for this work

CNRS

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	167-181
Number of pages	15
Journal	Pacific Journal of Mathematics
Volume	275
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2015.275.167
Publication status	Published - 2015

Keywords

Bers constant
Closed geodesic
Curvature-free inequalities
Isoperimetric inequalities
Width

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10.2140/pjm.2015.275.167

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abstract = "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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KW - Bers constant

KW - Closed geodesic

KW - Curvature-free inequalities

KW - Isoperimetric inequalities

KW - Width

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JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

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Measurements of Riemannian two-disks and two-spheres

Abstract

Keywords

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