Dictionary

Ahlfors theory en · NOUN

Etymology

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

Meanings

1. (qualifier:differential geometry, uncountable) 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.
   • 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:
   • 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:
   • 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:

Forms

wikipedia: Lars Ahlfors · wikipedia: Acta Mathematica