Stability of Gradient Kähler-Ricci Solitons

Albert Chau and Oliver Schnürer

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Submission date: 24. Apr. 2003
Pages: 30
published in: Communications in analysis and geometry, 13 (2005) 4, p. 769-800 
DOI number (of the published article): 10.4310/CAG.2005.v13.n4.a6
Bibtex
MSC-Numbers: 53C44, 58J37, 35B35
Keywords and phrases: kähler-ricci flow, soliton, stability
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Abstract:
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 -norm that decays for these barriers with non-negative Ricci curvature.