Analysis & Applied Math

Event Information Evolution of non-compact hypersurface by inverse mean curvature
14:10 on Friday October 18, 2019
15:00 on Friday October 18, 2019
BA6183, Bahen Center, 40 St. George St.
Beomjun Choi
https://sites.google.com/site/mathbeomjun/
University of Toronto

The inverse mean curvature flow has been studied for decades with fruitful application such as the proof of Riemannian Penrose inequality by Huisken-Ilmanen. In this talk, the existence and asymptotic behavior of convex non-compact flow will be discussed. The flow in non-compact setting would be one of natural things to ask, but less has been known toward this direction. The main difficulty lies in the type of diffusion the curvature follows, so called ultra fast-diffusion. The key ingredient to resolve this is an estimate on the inverse mean curvature in terms of the aperture of a supporting cone at infinity, and this gives regularity estimates up until the time the solution becomes flat. This is based on a joint work with P. Daskalopoulos.