Spheres of small diameter with long sweep-outs

Liokumovich, Yevgeny

doi:10.1090/S0002-9939-2012-11391-7

Spheres of small diameter with long sweep-outs
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by Yevgeny Liokumovich PDF

Proc. Amer. Math. Soc. 141 (2013), 309-312 Request permission

Abstract:

We prove the absence of a universal diameter bound on lengths of curves in a sweep-out of a Riemannian 2-sphere. If such a bound existed it would yield a simple proof of the existence of short geodesic segments and closed geodesics on a sphere of small diameter.

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