The length of the shortest closed geodesic on positively curved 2-spheres
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.
12 pages, 1 figure. Main result updated, typos corrected. Comments are welcome!