On holomorphic factorization and meromorphic selectors

Abstract

We show that, generically, a smooth Lorentzian 2 × 2 matrix valued function A, defined on the unit circle and possessing a so called exterior meromorphic section, can be extented into the unit disk in a way that admits a non-degenerate holomorphic factorization P ∗P , where the adjoint is taken with respect to the constant Lorentz matrix. This has implications for meromorphic approximation and Levi-flat surfaces with generalized disk fibers.