Surfaces of small diameter with large width
Differential Geometry
2013-11-15 v2
Abstract
Given a 2-dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M,g)=1 and every 1-cycle dividing M into two regions of equal area has length >C. It follows that there exists no universal inequality bounding 1-width of M in terms of its diameter. This answers a question of Stephane Sabourau.
Cite
@article{arxiv.1307.2306,
title = {Surfaces of small diameter with large width},
author = {Yevgeny Liokumovich},
journal= {arXiv preprint arXiv:1307.2306},
year = {2013}
}
Comments
15 pages, 5 figures. Improved exposition, corrected an error in the statement of Theorem 1.1, added an example due to Florent Balacheff. To appear in Journal of Topology and Analysis