Ahlfors theory

alternative Ahlfors' theory · alternative Ahlfors' theory of covering surfaces

1. uncountabledifferential geometrycomplex analysisA geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised "degree of covering") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric.

   Terms of the form o(A(r)) in Ahlfors theory are given in the form cD(r) where c is a constant.

   1986, Pacific Journal of Mathematics, volumes 122-123, page 441

   2 more examples

   In this chapter we use Ahlfors' theory of covering surfaces to obtain results on the functional n(r,a).

   1968, Joseph Belsley Miles, The Asymptotic Behavior of the Counting Function for the A-values of a Meromorphic Function, University of Wisconsin-Madison, page 29

   The Ahlfors theory itself describes covering of curves or domains, but not covering of distinct, complex values #92;boldsymbol#123;a#125;.

   2004, G. Barsegian, “A new program of investigations in analysis: Gamma-lines approaches”, in G. Barsegian, I. Laine, C. C. Yang, editors, Value Distribution Theory and Related Topics, Kluwer Academic, page 43