Inoue surfaces and the Chern-Ricci flow

TL;DR

This paper studies the behavior of the Chern-Ricci flow on Inoue surfaces, showing that it causes these non-Kähler surfaces to collapse to a circle over infinite time, revealing geometric evolution patterns.

Contribution

It demonstrates the long-term collapse of Inoue surfaces under the Chern-Ricci flow, a novel result in the study of non-Kähler complex surfaces.

Findings

Flow collapses surfaces to a circle at infinite time

Collapse occurs after an initial conformal change

Behavior characterized in the Gromov-Hausdorff sense

Abstract

We investigate the Chern-Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kahler compact complex surfaces of type Class VII. We show that, after an initial conformal change, the flow always collapses the Inoue surface to a circle at infinite time, in the sense of Gromov-Hausdorff.