Open Access
January 2015 On the evolution of a Hermitian metric by its Chern-Ricci form
Valentino Tosatti, Ben Weinkove
J. Differential Geom. 99(1): 125-163 (January 2015). DOI: 10.4310/jdg/1418345539


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.


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Valentino Tosatti. Ben Weinkove. "On the evolution of a Hermitian metric by its Chern-Ricci form." J. Differential Geom. 99 (1) 125 - 163, January 2015.


Published: January 2015
First available in Project Euclid: 12 December 2014

zbMATH: 1317.53092
MathSciNet: MR3299824
Digital Object Identifier: 10.4310/jdg/1418345539

Rights: Copyright © 2015 Lehigh University

Vol.99 • No. 1 • January 2015
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