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 Pierre Cousin 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.