The length of the shortest closed geodesic on positively curved 2-spheres

2020/06/08 by Adelstein, Ian, Pallete, Franco Vargas
#53C22 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.04849

Abstract

We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality for 2-spheres with pinched curvature; this allows us to improve our bound on the length of the shortest closed geodesic in the pinched curvature setting.

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