### Abstract

Original language | English |
---|---|

Number of pages | 13 |

Journal | arXiv |

Publication status | Published - 20 Apr 2017 |

### Fingerprint

### Keywords

- math.DG

### Cite this

*arXiv*.

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*arXiv*.

**Monotone contractions of the boundary of the disc.** / Chambers, E.W.; Chambers, G.R.; de Mesmay, A.; Ophelders, T.; Rotman, R.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Monotone contractions of the boundary of the disc

AU - Chambers, E.W.

AU - Chambers, G.R.

AU - de Mesmay, A.

AU - Ophelders, T.

AU - Rotman, R.

PY - 2017/4/20

Y1 - 2017/4/20

N2 - In this paper, we study contractions of the boundary of a Riemannian 2-disc where the maximal length of the intermediate curves is minimized. We prove that with an arbitrarily small overhead in the lengths of the intermediate curves, there exists such an optimal contraction that is monotone, i.e., where the intermediate curves are simple closed curves which are pairwise disjoint. This proves a conjecture of Chambers and Rotman.

AB - In this paper, we study contractions of the boundary of a Riemannian 2-disc where the maximal length of the intermediate curves is minimized. We prove that with an arbitrarily small overhead in the lengths of the intermediate curves, there exists such an optimal contraction that is monotone, i.e., where the intermediate curves are simple closed curves which are pairwise disjoint. This proves a conjecture of Chambers and Rotman.

KW - math.DG

M3 - Article

JO - arXiv

JF - arXiv

ER -