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MiS Preprint

Stability of Gradient Kähler-Ricci Solitons

Albert Chau and Oliver Schnürer


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

MSC Codes:
53C44, 58J37, 35B35
kähler-ricci flow, soliton, stability

Related publications

2005 Repository Open Access
Albert Chau and Oliver C. Schnürer

Stability of gradient Kähler-Ricci solitons

In: Communications in analysis and geometry, 13 (2005) 4, pp. 769-800