Riemann surfaces in Stein manifolds with the Density property
Annales de l'Institut Fourier, Volume 64 (2014) no. 2, p. 681-697

We show that any open Riemann surface can be properly immersed in any Stein manifold with the (Volume) Density property and of dimension at least 2. If the dimension is at least 3, we can actually choose this immersion to be an embedding. As an application, we show that Stein manifolds with the (Volume) Density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.

Nous montrons que toute surface de Riemann ouverte peut être immergée proprement dans toute variété de Stein avec la propriété de densité (volumique) et de dimension au moins 2. Si la dimension est au moins 3, cette immersion est en fait un plongement propre. Les résultats obtenus sont appliqués pour montrer que toutes les variétés de Stein avec la propriété de densité (volumique) et de dimension au moins 3 sont caractérisées entre toutes les variétés complexes par leur demi-groupe d’endomorphismes holomorphes.

DOI : https://doi.org/10.5802/aif.2862
Classification:  32H02,  32E30,  20M20
Keywords: Riemann surface, Stein manifold, proper holomorphic map, Andersen-Lempert theory, Density property, Volume Density property
@article{AIF_2014__64_2_681_0,
     author = {Andrist, Rafael B. and Wold, Erlend Forn\ae ss},
     title = {Riemann surfaces in Stein manifolds with the Density property},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     pages = {681-697},
     doi = {10.5802/aif.2862},
     mrnumber = {3330919},
     zbl = {06387289},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_2_681_0}
}
Andrist, Rafael B.; Wold, Erlend Fornæss. Riemann surfaces in Stein manifolds with the Density property. Annales de l'Institut Fourier, Volume 64 (2014) no. 2, pp. 681-697. doi : 10.5802/aif.2862. http://www.numdam.org/item/AIF_2014__64_2_681_0/

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