Monotone contractions of the boundary of the disc

E.W. Chambers, G.R. Chambers, A. de Mesmay, T. Ophelders, R. Rotman

Research output: Contribution to journalArticleAcademic

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Abstract

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.
Original languageEnglish
Number of pages13
JournalarXiv
Publication statusPublished - 20 Apr 2017

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Contraction
Monotone
Curve
Simple Closed Curve
Pairwise
Disjoint

Keywords

  • math.DG

Cite this

Chambers, E. W., Chambers, G. R., de Mesmay, A., Ophelders, T., & Rotman, R. (2017). Monotone contractions of the boundary of the disc. arXiv.
Chambers, E.W. ; Chambers, G.R. ; de Mesmay, A. ; Ophelders, T. ; Rotman, R. / Monotone contractions of the boundary of the disc. In: arXiv. 2017.
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Chambers, EW, Chambers, GR, de Mesmay, A, Ophelders, T & Rotman, R 2017, 'Monotone contractions of the boundary of the disc', arXiv.

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

In: arXiv, 20.04.2017.

Research output: Contribution to journalArticleAcademic

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

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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.

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Chambers EW, Chambers GR, de Mesmay A, Ophelders T, Rotman R. Monotone contractions of the boundary of the disc. arXiv. 2017 Apr 20.