Title: The Chern-Ricci flow on primary Hopf surfaces
2019.06.14 |
| Date | Thu 27 Jun |
| Time | 09:15 — 10:15 |
| Location | 1531-215 (Aud-D3) |
Abstract:
The Chern-Ricci flow is a flow of Hermitian metrics which generalizes the Kähler-Ricci flow to non-Kähler metrics. While solutions of the flow have been classified on many families of complex non-Kähler surfaces, the Hopf surfaces provide a family of non-Kähler surfaces on which little is known about the Chern-Ricci flow. We use a construction of locally conformally Kähler metrics of Gauduchon-Ornea to study solutions of the Chern-Ricci flow on primary 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 established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.
