Ahlfors theory

Ahlfors theory

English

Alternative forms

• Ahlfors' theory
• Ahlfors' theory of covering surfaces

Etymology

Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.[1]

Noun

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, 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 ${\\displaystyle {\\boldsymbol {a}}}$.

Translations

theory that extends the concept of covering surface

References

1. 1935, "Zur Theorie der Uberlagerungsflachen", Acta Mathematica, Volume 65, 157–194.