EVENT DETAILS AND ABSTRACT

Title: The Chern-Ricci flow on primitive Hopf surfaces
Speaker: Gregory Edwards
Speaker Info: Notre Dame
Brief Description:
Special Note:
Abstract:

The Chern-Ricci flow is a flow of Hermitian metrics which generalizes the Kahler-Ricci flow to non-Kahler metrics. While solutions of the flow have been classified on some families non-Kahler surfaces, the Hopf surfaces provide a family of non-Kahler surfaces on which little is known about the Chern-Ricci flow. We use a construction of locally conformally Kahler metrics of Gauduchon-Ornea to study solutions of the Chern-Ricci flow on primitive Hopf surfaces of class 1. These solutions reach a volume collapsing singularity in finite time, and we show that the metric tensor satisfies a uniform upper bound, supporting the conjecture that the Gromov-Hausdorff limit is isometric to a round S^1. Uniform C^{1+\beta} estimates are also established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.