

Preprint 39/2003
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.