Tuesday, September 15, 2020
09/15/2020 - 4:00pm
We'll start with an intuitive introduction to the isosystolic inequalities. We then 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. This is joint work with Franco Vargas Pallete.