Monotone contractions of the boundary of the disc

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

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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

Keywords

  • math.DG

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