Andersen-Lempert理论的现状
On the present state of the Andersen-Lempert theory
摘要：
在Andersen-Lempert理论的综述中，我们介绍了密度性质研究的最新进展（这意味着由给定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空间中是稠密的）。本文还得到了两个新的结果，其中之一是证明了具有体密度性质的Stein流形的乘积也具有体密度性质。第二个例子是一个没有代数密度性质的代数曲面的有意义的例子。最后一个事实的证明需要布鲁内拉的技术。
英文摘要：
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.
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