论文标题
阳性和几乎是亚伯族复合物的阳性冬宫曲率流
Positive Hermitian Curvature Flow on nilpotent and almost-abelian complex Lie groups
论文作者
论文摘要
我们研究了复杂的谎言组左右指标的空间上的阳性均曲率流。我们表明，在尼尔疗法的情况下，在所有积极时期都存在该流量，并在cheeger-gromov的感觉中以孤儿的身份进行了子会议。当复杂的谎言组几乎是阿贝利安时，我们还表现出与孤儿的融合。也就是说，当它的谎言代数承认（复杂的）共同维度一个Abelian理想时。最后，我们在几乎亚伯式的环境中研究孤子。我们证明了唯一性，并完全对所有剩下的，几乎是亚伯式的孤儿进行了分类，提供了一种在任意维度中构造示例的方法，其中许多允许共同处理晶格。
We study the positive Hermitian curvature flow on the space of left-invariant metrics on complex Lie groups. We show that in the nilpotent case, the flow exists for all positive times and subconverges in the Cheeger-Gromov sense to a soliton. We also show convergence to a soliton when the complex Lie group is almost abelian. That is, when its Lie algebra admits a (complex) co-dimension one abelian ideal. Finally, we study solitons in the almost-abelian setting. We prove uniqueness and completely classify all left-invariant, almost-abelian solitons, giving a method to construct examples in arbitrary dimensions, many of which admit co-compact lattices.
