Stability of gradient Kähler-Ricci solitons

Abstract

We study stability of non-compact gradient Kahler-Ricci ow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kahler potential of the soliton will con- verge to the original soliton under Kahler-Ricci ow as time tends to innity. To obtain this result, we construct appropriate barriers and introduce an L p -norm that decays for these barriers with non-negative Ricci curvature.