Ancient solution to Kahler-Ricci flow

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In this paper, we prove that any non-flat ancient solution to Kähler-Ricci flow with bounded nonnegative bisectional curvature has asymptotic volume ratio zero. We also prove that any gradient shrinking solitons with positive bisectional curvature must be compact. Both results generalize the corresponding earlier results of Perelman in \cite{P1} and \cite{P2}. The results can be applied to study the geometry and function theory of complete Kähler manifolds with nonnegative bisectional curvature via Kähler-Ricci flow. It also implies a compactness theorem on ancient solutions to Kähler-Ricci flow.
We sharpen the statement of the result on shrinking solitons in this newer version

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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/74296

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502494
 http://arxiv.org/abs/math/0502494

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arXiv