Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 859-871

ON THE SECOND MAIN THEOREM OF CARTAN

Alexandre Eremenko

Purdue University, Department of Mathematics
West Lafayette, IN 47907, U.S.A.; eremenko 'at' math.purdue.edu

Abstract. The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a class of holomorphic curves defined by solutions of linear differential equations.

2010 Mathematics Subject Classification: Primary 30D35, 32A22.

Key words: Nevanlinna theory, Second Main theorem, linear differential equations.

Reference to this article: A. Eremenko: On the Second Main Theorem of Cartan. Ann. Acad. Sci. Fenn. Math. 39 (2014), 859-871.

Full document as PDF file

doi:10.5186/aasfm.2014.3937