We investigate the Kähler–Ricci flow modified by a holomorphic vector field. We find equivalent analytic criteria for the convergence of the flow to a Kähler–Ricci soliton. In addition, we relate the asymptotic behavior of the scalar curvature along the flow to the lower boundedness of the modified Mabuchi energy.
Cite this article
D. H. Phong, Jian Song, Jacob Sturm, Ben Weinkove, On the convergence of the modified Kähler–Ricci flow and solitons. Comment. Math. Helv. 86 (2011), no. 1, pp. 91–112DOI 10.4171/CMH/219