Geometria Complessa e Geometria Differenziale
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D. Angella - V. Tosatti

Leafwise flat forms on Inoue-Bombieri surfaces

created by daniele on 01 Jul 2021
modified on 21 Jul 2023


Published Paper

Inserted: 1 jul 2021
Last Updated: 21 jul 2023

Journal: J. Funct. Anal.
Volume: 285
Number: 5
Pages: 34 pp.
Year: 2023
Doi: 10.1016/j.jfa.2023.110015

ArXiv: 2106.16141 PDF

Paper No. 1100


We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its $\partial\overline\partial$-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 $\partial\overline\partial$-class of the TricerriVaisman metric.

Tags: SIR2014-AnHyC

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