Riemann surfaces in Stein manifolds with density property

Details Riemann surfaces in Stein manifolds with density property Riemann surfaces in Stein manifolds with density property

2011-06-22

arxiv.org/abs/1106.4416v1

Mathematics

Complex Variables

13 pages, 5 figures

Scientific paper

It is shown that any open Riemann surface can be immersed in any Stein manifold with (volume) density property and of dimension at least 2, if the manifold possesses an exhaustion with holomorphically convex compacts such that their complement is connected. The immersion can be made into an embedding if the dimension is at least 3. As an application, it is shown that Stein manifolds with (volume) density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.

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