On the present state of the Andersen-Lempert theory
On the present state of the Andersen-Lempert theory
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关于安徒生-伦珀特理论的现状
DOI：
10.1090/crmp/054/07
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
F. Kutzschebauch
中科院分区：
文献类型：
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作者：
S. Kaliman;F. Kutzschebauch
在Andersen-Lempert理论的综述中，我们介绍了密度性质(即由给定的Stein流形上的完全可积全纯向量场生成的李代数在所有全纯向量场的空间中稠密)的研究现状。本文还得到了两个新结果，其中一个是关于体密度性质的Stein流形的乘积也具有这一性质的定理。第二个例子是没有代数密度性质的代数曲面的一个有意义的例子。最后一个事实的证明需要布鲁内拉的技术。
In this survey of the Andersen-Lempert theory we present the state of the art in the study of the density property (which means that the Lie algebra generated by completely integrable holomorphic vector fields on a given Stein manifold is dense in the space of all holomorphic vector fields). There are also two new results in the paper one of which is the theorem stating that the product of Stein manifolds with the volume density property possesses such a property as well. The second one is a meaningful example of an algebraic surface without the algebraic density property. The proof of the last fact requires Brunella's technique.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
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作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest