Stability of gradient Kähler-Ricci solitons


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CHAU, Albert, Oliver C. SCHNÜRER, 2005. Stability of gradient Kähler-Ricci solitons. In: Communications in Analysis and Geometry. 13(4), pp. 769-800. ISSN 1019-8385. eISSN 1944-9992. Available under: doi: 10.4310/CAG.2005.v13.n4.a6

@article{Chau2005Stabi-41145, title={Stability of gradient Kähler-Ricci solitons}, year={2005}, doi={10.4310/CAG.2005.v13.n4.a6}, number={4}, volume={13}, issn={1019-8385}, journal={Communications in Analysis and Geometry}, pages={769--800}, author={Chau, Albert and Schnürer, Oliver C.} }

Chau, Albert Schnürer, Oliver C. We study the stability of non-compact gradient K¨ahler–Ricci solitons under the Kähler–Ricci flow. Our main result is that appropriate perturbations of Cao’s steady soliton metric on C<sup>n</sup> will converge to the original soliton under the Kähler–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 Lp-norm that decays for these barriers with non-negative Ricci curvature. Chau, Albert eng 2018-01-25T08:06:04Z Stability of gradient Kähler-Ricci solitons 2005 Schnürer, Oliver C. 2018-01-25T08:06:04Z

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