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Several Complex Variables

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4 domain-specific abstractions whose origin domain is Several Complex Variables.

  • Bochner–Martinelli formula — An integral representation for continuously differentiable functions on domains in several complex variables using the Bochner–Martinelli kernel.
  • Cousin problems — Ask whether compatible local meromorphic data on a complex manifold glue to a global meromorphic function, with additive and multiplicative versions carrying distinct cohomological obstructions.
  • Ohsawa–Takegoshi L2 extension theorem — A theorem extending square-integrable holomorphic functions from a complex submanifold with controlled norm.
  • Pluriharmonic function — A function on a complex manifold whose restriction to every complex line is harmonic, locally the real part of a holomorphic function in the real-valued case.