论文信息 - Monotone contractions of the boundary of the disc

Monotone contractions of the boundary of the disc

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.

Erin W. Chambers | Arnaud de Mesmay | Tae Tim Ophelders | Regina Rotman | Gregory R. Chambers

[1] Peter Winkler,et al. Submodular Percolation , 2009, SIAM J. Discret. Math..

[2] Erin W. Chambers,et al. Measuring similarity between curves on 2-manifolds via homotopy area , 2013, SoCG '13.

[3] Erin W. Chambers,et al. On the Height of a Homotopy , 2009, CCCG.

[4] Erin W. Chambers,et al. Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time , 2010, Comput. Geom..

[5] Yevgeny Liokumovich,et al. Converting homotopies to isotopies and dividing homotopies in half in an effective way , 2013, 1311.0779.

[6] Regina Rotman,et al. Contracting loops on a Riemannian 2-surface , 2013 .

[7] Amir Nayyeri,et al. How to walk your dog in the mountains with no magic leash , 2012, SoCG '12.