Title:
The Length of a Shortest Closed Geodesic on a Surface of Finite Area
Abstract: Every complete surface of finite area admits at least
one closed (periodic) geodesic. It is natural to ask how long these
curves can be relative to the surface's total area, and it is easiest
to consider the length of a (possibly non-unique) shortest
geodesic. One approach is to utilize the Birkhoff curve shortening
process. However, the non-compact case presents a challenge, as a
given curve may escape to infinity under the curve shortening process
instead of converging to a geodesic. In this talk, we present joint
work with Regina Rotman on this problem that builds upon the results
of Christopher Croke. We also explore other contexts in which the
presented techniques can be applied.