On the stability of the anomaly flow

Abstract

We prove that the parabolic flow of conformally balanced metrics introduced by Phong, Picard and Zhang in "A flow of conformally balanced metrics with Kähler fixed points", is stable around Calabi-Yau metrics. The result shows that the flow can converge on a Kähler manifold even if the initial metric is not conformally Kähler.

arXiv comment10 pages. Final Version. To appear in Mathematical Research Letters Vol.29, no.2