Ahlfors theory

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Ahlfors theory

Wikipedia

• Ahlfors' theory
• Ahlfors' theory of covering surfaces

Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.

Ahlfors theory (uncountable)

1. (complex analysis, differential geometry) A 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.
   • 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:

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

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

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

   • 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:

     The Ahlfors theory itself describes covering of curves or domains, but not covering of distinct, complex values ${\displaystyle {\boldsymbol {a}}}$.