The modified Kähler-Ricci flow and solitons

Details The modified Kähler-Ricci flow and solitons The modified Kähler-Ricci flow and solitons

2008-09-05

arxiv.org/abs/0809.0941v1

Mathematics

Differential Geometry

33 pages

Scientific paper

We investigate the K\"ahler-Ricci flow modified by a holomorphic vector
field. We find equivalent analytic criteria for the convergence of the flow to
a K\"ahler-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.

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