Title: The affine shape of a figure8 under the curve shortening flow
Abstract: We study the behavior of a natural class of figure-eight curves evolving by the Curve-Shortening Flow.
We examine the asymptotic behavior and show that suitably chosen arcs of our evolving curves, when suitably rescaled, converge to the Grim Reaper Soliton. Using the Grim Reaper Theorem and auxiliary curvature estimates, we show that when affine rescalings are applied to our solution to keep the aspect ratio equal to one, the limit converges to a quadrilateral called a "bowtie". This is joint work with Richard Schwartz.