The modified Kähler-Ricci flow and solitons

Abstract

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.

33 pages

References in corpus (1)

• Kähler-Ricci flow on a toric manifold with positive first Chern class

Cited by in corpus (3)

• Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold
• Kähler Ricci flow on Fano manifolds with vanished Futaki invariants
• Kähler Ricci flow with vanished Futaki invariant