Inoue surfaces and the Chern–Ricci flow

Shouwen Fang (1) , Valentino Tosatti (2) , Ben Weinkove (3) , Tao Zheng (4)

1 Yangzhou University
2 Department of Mathematics, Northwestern University
3 Northwestern University [Evanston]
4 IF - Institut Fourier

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.

Domaines: Mathématiques [math]

Shouwen Fang, Valentino Tosatti, Ben Weinkove, Tao Zheng. Inoue surfaces and the Chern–Ricci flow. Journal of Functional Analysis, 2016, 271 (11), pp.3162 - 3185. ⟨10.1016/j.jfa.2016.08.013⟩. ⟨hal-01680410⟩