Inoue surfaces and the Chern-Ricci flow

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.

23 pages

References in corpus (3)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• The Dirichlet problem for degenerate complex Monge-Ampere equations
• Collapsing of Products Along the Kähler-Ricci Flow

Cited by in corpus (12)

• The Anomaly flow over Riemann surfaces
• The Chern-Ricci flow on Oeljeklaus-Toma manifolds
• The Chern-Ricci flow and holomorphic bisectional curvature
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• Chern-Ricci flows on noncompact complex manifolds
• A parabolic Monge-Ampère type equation of Gauduchon metrics
• Hermitian curvature flow on complex locally homogeneous surfaces
• Levi-Civita Ricci-flat metrics on compact complex manifolds
• Minimal complex surfaces with Levi-Civita Ricci-flat metrics
• Weak Solutions of the Chern-Ricci flow on compact complex surfaces
• Leafwise flat forms on Inoue-Bombieri surfaces
• The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature and Oeljeklaus-Toma manifolds