Spheres of small diameter with long sweep-outs
classification
🧮 math.DG
keywords
diameterboundsmallsphereabsenceclosedcurvesexisted
read the original 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 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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