On the evolution of a Hermitian metric by its Chern-Ricci form
On the evolution of a Hermitian metric by its Chern-Ricci form
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DOI：
10.4310/jdg/1418345539
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发表时间：
2011-12
影响因子：
2.5
通讯作者：
Valentino Tosatti;B. Weinkove
中科院分区：
文献类型：
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作者：
Valentino Tosatti;B. Weinkove
我们考虑紧致复流形上的厄米度量通过其Chern-Ricci形式的演化。这是一个由M.Gill首先研究的演化方程，如果初始度规是Kahler，则它与Kahler-Ricci流重合。我们根据初始数据求出了流的最大生存时间。我们研究了当初始度量为Gauduchon时，在具有负第一类的复流形上以及在一些Hopf流形上流动的行为。最后，我们讨论了Hermite流形上复Monge-Ampere方程的一个新估计。
We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kahler-Ricci flow if the initial metric is Kahler. We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampere equation on Hermitian manifolds.