
Something like Picard for 1-forms
Conjecture Let
be the open unit disk in the complex plane and let
be open sets such that
. Suppose there are injective holomorphic functions
such that for the differentials we have
on any intersection
. Then those differentials glue together to a meromorphic 1-form on
.








It is an evidence that the 1-form is holomorphic on . In the case that its residue at the origin vanishes we can use Picard's big theorem.
Bibliography
*B. Elsner: Hyperelliptic action integral, Annales de l'institut Fourier 49(1), p.303–331
* indicates original appearance(s) of problem.