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arXiv · 1411.6349

Optimal sweepouts of a Riemannian 2-sphere

Gregory R. Chambers·Yevgeny Liokumovich
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Abstract

Given a sweepout of a Riemannian 2-sphere which is composed of curves of length less than L, we construct a second sweepout composed of curves of length less than L which are either constant curves or simple curves. This result, and the methods used to prove it, have several consequences; we answer a question of M. Freedman concerning the existence of min-max embedded geodesics, we partially answer a question due to N. Hingston and H.-B. Rademacher, and we also extend the results of [CL] concerning converting homotopies to isotopies in an effective way.

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Gregory R. Chambers, Yevgeny Liokumovich. 2014-11-24. Optimal sweepouts of a Riemannian 2-sphere. https://arxiv.org/abs/1411.6349

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