Stability of gradient Kahler-Ricci solitons

摘要

We study the stability of non-compact gradient Kahler-Ricci solitons under the Kahler-Ricci flow. Our main result is that appropriate perturbations of Cao's steady soliton metric on C-n will converge to the original soliton under the Kahler-Ricci flow as time tends to infinity. These perturbations correspond to appropriately decaying perturbations of the soliton potential function; in particular, this includes any compactly supported perturbation. To obtain this result, we construct appropriate barriers and introduce an L-p-norm that decays for these barriers with non-negative Ricci curvature.