The density property for complex manifolds and geometric structures

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Criteria for the density property of complex manifolds (2007, background): “[16] A. Toth, D. Varolin, Holomorphic diffeomorphisms of semisimple homogenous spaces, arXiv:math.”
On the present state of the Andersen-Lempert theory (2010, background): “In the sequence of papers ([70], [67], [68], [44], [45], [21]) the algebraic density property was established for a wide variety of affine algebraic manifolds, including all homogeneous spaces that coincide with quotients of linear algebraic groups with respect to their reductive subgroups provided ”
Holomorphic flexibility properties of complex manifolds (2004, background): “a property of Y imply the Oka property of Y0? What is the answer for ﬁnitely sheeted π? 6.8. The density property and the Oka property. We mention another ﬂexibility property introduced by D. Varolin [78], [79] (motivated by results of And´ersen and Lempert on holomorphic automorphisms of Cn [2]) an”
Flexible varieties and automorphism groups (2010, background): “13], [39]) Let a Stein manifold X of dimension ≥ 2 possess the density property.”
Noncritical holomorphic functions on Stein manifolds (2002, result): “um of complete holomorphic ﬁelds in the w-variable. The products of such ﬁelds with zα are complete on Cn which proves the result. Remark. For a more general result in this direction see Lemma 2.5 in [V]. A similar result can be found in the recent preprint [Ku]. Lemma 3.5 implies that the time-tmap”