Manifolds of holomorphic mappings from strongly pseudoconvex domains

By F. Forstnerič. 2006

50 citations recorded by the source corpus.

Let D be a bounded strongly pseudoconvex domain in a Stein manifold S and let Y be a complex manifold. We prove that the graph of any continuous map from the closure of D to Y which is holomorphic in D admits a basis of open Stein neighborhoods in S x Y. Using this we show that many classical spaces of maps from the closure of D to Y which are holomorphic in D are infinite dimensional complex manifolds which are modeled on locally convex topological vector spaces (Banach, Hilbert or Frechet).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cd8f8eca04cc08c88ae636ed24e0b976dc602282

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan (2018, background): “ class Ar(S,Y)for any r ∈ N. ⊓⊔ In the special case when the strongly admissible set K =S is the closure of a relatively compact strongly pseudoconvex domain, Corollary 9 was proved by F. Forstnericˇ [58]in2007.His proofis differentfromthoseabovewhichrelyonPoletsky’sTheorem32.Insteaditusesthemethodo”