Complex Analysis with differential forms

Question

I'm studying a little of Complex Analysis and I have seen that I can use the integrals of complex functions as integrals of differential forms in $\mathbb{R}^n.$ For example: Cauchy Theorem for complex analytic functions is a consequence of the fact that a closed differential form on a simply connected set is exact.

My question is : Are there other famous theorem of Complex Analysis that I can prove with the theory of differential forms in Euclidean space?

Answer 1

One such book is H. Cartan, Elementary theory of analytic functions of one or several complex variables, Paris, Herman, 1963.