2014•Journal of Topology and AnalysisOpen access
Surfaces of small diameter with large width
Yevgeny Liokumovich
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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 Stéphane Sabourau.
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