Spheres of small diameter with long sweep-outs

Details Spheres of small diameter with long sweep-outs Spheres of small diameter with long sweep-outs

2011-05-31

arxiv.org/abs/1105.6159v1

Mathematics

Differential Geometry

Scientific paper

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

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