Commentarii Mathematici Helvetici


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Volume 86, Issue 1, 2011, pp. 91–112
DOI: 10.4171/CMH/219

Published online: 2010-12-05

On the convergence of the modified Kähler–Ricci flow and solitons

D. H. Phong[1], Jian Song[2], Jacob Sturm[3] and Ben Weinkove[4]

(1) Columbia University, New York, USA
(2) Rutgers University, Piscataway, USA
(3) Rutgers University, Newark, USA
(4) University of California, San Diego, La Jolla, USA

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.

Keywords: Kähler–Ricci flow, soliton, Mabuchi energy.

Phong D., Song Jian, Sturm Jacob, Weinkove Ben: On the convergence of the modified Kähler–Ricci flow and solitons. Comment. Math. Helv. 86 (2011), 91-112. doi: 10.4171/CMH/219