Inoue surfaces and the Chern–Ricci flow

Shouwen Fang; Valentino Tosatti; Ben Weinkove; Tao Zheng

doi:10.1016/j.jfa.2016.08.013

Inoue surfaces and the Chern–Ricci flow

Shouwen Fang, Valentino Tosatti, Ben Weinkove^*, Tao Zheng

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kähler 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.

Original language	English (US)
Pages (from-to)	3162-3185
Number of pages	24
Journal	Journal of Functional Analysis
Volume	271
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2016.08.013
State	Published - Dec 1 2016

Funding

Supported in part by National Science Foundation of China grants 11401514 (S.F) and 11401023 (T.Z.), and National Science Foundation grants DMS-1308988 (V.T.) and DMS-1406164 (B.W). The second-named author is supported in part by a Sloan Research Fellowship .

Keywords

Chern–Ricci flow
Class VII surfaces
Inoue surfaces

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2016.08.013

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abstract = "We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-K{\"a}hler 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.",

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AU - Weinkove, Ben

AU - Zheng, Tao

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N2 - We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kähler 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.

AB - We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kähler 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.

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KW - Class VII surfaces

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Inoue surfaces and the Chern–Ricci flow

Abstract

Funding

Keywords

ASJC Scopus subject areas

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