Spheres of small diameter with long sweep-outs

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.

References in corpus (1)

• Diastolic and isoperimetric inequalities on surfaces

Cited by in corpus (1)

• Contracting the boundary of a Riemannian 2-disc