Abstract:
Self-expanding solutions of curvature flows evolve by homothetic expansions under the flow. Rotational symmetric examples are constructed by Ecker-Huisken, Angenent-Chopp-Ilmanen, Helmensdorfer et. al for the Mean Curvature Flow, and by Huisken-Ilmanen, Grugan-Lee-Wheeler et. al for the Inverse Mean Curvature Flow. Many known examples are asymptotic to some standard models such as round cylinders and round cones. In this talk, the speaker will talk about rotational rigidity results for self-expanders of both Mean Curvature and Inverse Mean Curvature Flows, proving that certain self-expanders asymptotic to cones or cylinders are necessarily rotational symmetric. These are joint works with Peter McGrath, and with Gregory Drugan and Hojoo Lee.