Ahlfors finiteness theorem

Ahlfors' finiteness theorem is a result in complex analysis and several complex variables, particularly in the study of Riemann surfaces and compact complex manifolds. The theorem is named after Lars Ahlfors, a prominent mathematician known for his contributions to complex analysis. The theorem essentially states that for a compact Riemann surface (or a compact complex manifold), the number of non-constant meromorphic functions (or rational functions) that can be defined on it is finite.