Archiv der Mathematik

, Volume 89, Issue 4, pp 326–338 | Cite as

Envelope of holomorphy for boundary cross sets



Let \(D\subset{\mathbb{C}}^n, G\subset{\mathbb{C}}^m\) be open sets, let A (resp. B) be a subset of the boundary ∂D (resp. ∂G) and let W be the 2-fold boundary cross \(((D\cup A)\times B) \cup (A \times (B \cup G))\). An open subset \(X \subset {{\mathbb{C}}^{n+m}}\) is said to be the “envelope of holomorphy” of W if it is, in some sense, the maximal open set with the following property: Any function locally bounded on W and separately holomorphic on \((A \times G) \cup (D \times B)\) “extends” to a holomorphic function defined on X which admits the boundary values f a.e. on W. In this work we will determine the envelope of holomorphy of some boundary crosses.

Mathematics Subject Classification (2000).

Primary 32D15 32D10 


Boundary cross set envelope of holomorphy holomorphic extension plurisubharmonic measure 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Institut für MathematikCarl von Ossietzky Universität OldenburgOldenburgGermany
  2. 2.Mathematics SectionThe Abdus Salam international centre for theoretical physicsTriesteItaly

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