Several complex variables | Complex analysis | Sheaf theory

Cousin problems

In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in special cases by in 1895. They are now posed, and solved, for any complex manifold M, in terms of conditions on M. For both problems, an open cover of M by sets Ui is given, along with a meromorphic function fi on each Ui. (Wikipedia).

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Related pages

Complex plane | Cartan's theorems A and B | Riemann surface | Stein manifold | Weierstrass factorization theorem | Mathematics | Line bundle | Chern class | Holomorphic function | Sheaf cohomology | Exponential sheaf sequence | Sheaf (mathematics) | Logarithm | Meromorphic function | Abelian group | Function of several complex variables | Complex manifold