Tuesday September 28th, 2021 | |
Time: | 4:30 PM - 5:30 PM |
Title: | Ricci flow on noncompact surfaces with rough initial data |
Speaker: | Peter Topping, University of Warwick, UK |
Location: | Online |
Abstract: | |
There has been much work in recent years on starting the Ricci flow with initial data that is rougher than a Riemannian metric. There has also been significant development of Ricci flow theory on noncompact manifolds. In this talk I will describe some recent work joint with Hao Yin in two dimensions that tackles these topics simultaneously. We replace the initial Riemannian metric with a combination of a complex structure and a nonatomic Radon measure. An important aspect is to derive suitable a priori estimates for the logarithmic fast diffusion equation. I will also use the theory to generate a large new class of Ricci solitons, and to resolve an open problem concerning Ricci flow regularity. |