In this work, we obtain existence criteria for Chern-Ricci flows on noncompact manifolds. We generalize a result by Tossati-Wienkove on Chern-Ricci flows to noncompact manifolds and at the same time generalize a result for Kahler-Ricci flows by Lott-Zhang to Chern-Ricci flows. Using the existence results, we prove that any complete noncollapsed Kahler metric with nonnegative bisectional curvature on a noncompact complex manifold can be deformed to a complete Kahler metric with nonnegative and bounded bisectional curvature which will have maximal volume growth if the initial metric has maximal volume. Combining this result with the result of Chau-Tam, we give another proof that a complete noncompact Kahler manifold with nonnegative bisectional curvature (not necessarily bounded) and maximal volume growth is biholomorphic to the complex Euclidean space. This last result has already been proved by Gang Liu recently using other methods. This last result is partial confirmation of a uniformization conjecture of Yau.

中文翻译：

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Chern-Ricci 在非紧复流形上流动

在这项工作中，我们获得了非紧流形上 Chern-Ricci 流的存在标准。我们将 Tossati-Wienkove 对 Chern-Ricci 流的结果推广到非紧流形，同时将 Lott-Zhang 对 Kahler-Ricci 流的结果推广到 Chern-Ricci 流。使用存在性结果，我们证明了在非紧复流形上具有非负二分曲率的任何完全非塌陷 Kahler 度量可以变形为具有非负和有界二分曲率的完全 Kahler 度量，如果初始度量具有最大体积，则该度量将具有最大体积增长。将此结果与 Chau-Tam 的结果相结合，我们给出了另一个证明，具有非负二分曲率（不一定有界）和最大体积增长的完全非紧卡勒流形是复欧几里得空间的双全纯。刘刚最近使用其他方法已经证明了最后一个结果。最后一个结果部分证实了丘的均匀化猜想。