具有无界曲率的变形完全Hermitian度量
Deforming complete Hermitian metrics with unbounded curvature
摘要：
我们产生的里奇流的解决方案出现从完整的初始度量$g_0$这是$C^0$埃尔米特限制的Kähler度量。特别感兴趣的是当$g_0$是具有无界曲率的Kähler。我们提供了这样的解决方案，广泛的一类$U(n)$不变的Kähler度量$g_0$的$n$维复欧几里得空间，其中许多具有无界曲率。作为特例，我们得到了如下推论：从$\C^n$上的任意光滑完备$U(n)$ -不变Käbler度量出发，在全纯双截曲率为非负或非正的情况下，里奇流存在光滑短时解，并且在非正曲率的情况下，该解存在于所有时间.
英文摘要：
We produce solutions to the Kähler-Ricci flow emerging from complete initial metrics $g_0$ which are $C^0$ Hermitian limits of Kähler metrics. Of particular interest is when $g_0$ is Kähler with unbounded curvature. We provide such solutions for a wide class of $U(n)$-invariant Kähler metrics $g_0$ on $n$ dimensional complex Euclidean space, many of which having unbounded curvature. As a special case we have the following Corollary: The Kähler-Ricci flow has a smooth short time solution starting from any smooth complete $U(n)$-invariant Käbler metric on $\C^n$ with either non-negative or non-positive holomorphic bisectional curvature, and the solution exists for all time in the case of non-positive curvature.
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