Journal of Differential Geometry

On the evolution of a Hermitian metric by its Chern-Ricci form

Valentino Tosatti and Ben Weinkove

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Abstract

We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kähler-Ricci flow if the initial metric is Kähler. We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampère equation on Hermitian manifolds.

Article information

Source
J. Differential Geom., Volume 99, Number 1 (2015), 125-163.

Dates
First available in Project Euclid: 12 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1418345539

Digital Object Identifier
doi:10.4310/jdg/1418345539

Mathematical Reviews number (MathSciNet)
MR3299824

Zentralblatt MATH identifier
1317.53092

Citation

Tosatti, Valentino; Weinkove, Ben. On the evolution of a Hermitian metric by its Chern-Ricci form. J. Differential Geom. 99 (2015), no. 1, 125--163. doi:10.4310/jdg/1418345539. https://projecteuclid.org/euclid.jdg/1418345539


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