On dimension reduction in the Kähler-Ricci flow

Huai-Dong Cao

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On dimension reduction in the Kähler-Ricci flow

Huai-Dong Cao

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Abstract

We consider dimension reduction for solutions of the Kähler-Ricci flow with nonegative bisectional curvature. When the complex dimension $n=2$, we prove an optimal dimension reduction theorem for complete translating Kähler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reduction theorem for complete ancient solutions of the Kähler-Ricci flow with nonnegative bisectional curvature on noncompact complex manifolds under a finiteness assumption on the Chern number $c^n_1$.

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Huai-Dong Cao. 2003-02-11. On dimension reduction in the Kähler-Ricci flow. https://arxiv.org/abs/math/0302112

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