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

Geometry Topology Seminar
Monday, April 26, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Franco Vargas Pallete – Yale University – franco.vargaspallete@yale.eduhttps://gauss.math.yale.edu/~fv63/
Beibei Liu

Following the approach of Nabutovsky and Rotman for the curve-shortening flow on geodesic nets, we'll show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. On the pinched curvature setting, we prove a bound on the first eigenvalue of the Laplacian and use it to prove a new isoperimetric inequality for pinched 2-spheres sufficiently close to being round. 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 Ian Adelstein.