Leafwise flat forms on Inoue-Bombieri surfaces

Daniele Angella; Valentino Tosatti

doi:10.1016/j.jfa.2023.110015

Leafwise flat forms on Inoue-Bombieri surfaces

Daniele Angella, Valentino Tosatti

Mathematics

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

Abstract

We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its ∂∂‾-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the ∂∂‾-class of the Tricerri/Vaisman metric.

Original language	English (US)
Article number	110015
Journal	Journal of Functional Analysis
Volume	285
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2023.110015
State	Published - Sep 1 2023

Keywords

Chern-Ricci flow
Gauduchon metric
Inoue-Bombieri surface
Leafwise flat form

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2023.110015

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title = "Leafwise flat forms on Inoue-Bombieri surfaces",

abstract = "We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its ∂∂‾-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the ∂∂‾-class of the Tricerri/Vaisman metric.",

keywords = "Chern-Ricci flow, Gauduchon metric, Inoue-Bombieri surface, Leafwise flat form",

author = "Daniele Angella and Valentino Tosatti",

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doi = "10.1016/j.jfa.2023.110015",

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AU - Angella, Daniele

AU - Tosatti, Valentino

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Y1 - 2023/9/1

N2 - We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its ∂∂‾-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the ∂∂‾-class of the Tricerri/Vaisman metric.

AB - We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its ∂∂‾-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the ∂∂‾-class of the Tricerri/Vaisman metric.

KW - Chern-Ricci flow

KW - Gauduchon metric

KW - Inoue-Bombieri surface

KW - Leafwise flat form

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JO - Journal of Functional Analysis

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M1 - 110015

ER -

Leafwise flat forms on Inoue-Bombieri surfaces

Abstract

Keywords

ASJC Scopus subject areas

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