Chern–Ricci flows on noncompact complex manifolds

In this work, we obtain existence criteria for Chern–Ricci flows on noncompact manifolds. We generalize a result by Tossati–Wienkove 37 on Chern-Ricci flows to noncompact manifolds and a result for Kähler–Ricci flows by Lott–Zhang 21 to Chern–Ricci flows. Using the existence results, we prove that any complete noncollapsed Kähler metric with nonnegative bisectional curvature on a noncompact complex manifold can be deformed to a complete Kähler metric with nonnegative and bounded bisectional curvature which will have maximal volume growth if the initial metric has maximal volume growth. Combining this result with 3, we give another proof that a complete noncompact Kähler manifold with nonnegative bisectional curvature (not necessarily bounded) and maximal volume growth is biholomorphic to ⁿ. This last result has already been proved by Liu 20 recently using other methods. This last result is a partial confirmation of a uniformization conjecture of Yau 41.