On the second main theorem of Cartan

TL;DR

This paper discusses reversing the inequality in Cartan's Second Main Theorem and introduces a new version that approaches equality for certain holomorphic curves defined by linear differential equations.

Contribution

It presents a new version of Cartan's Second Main Theorem that becomes asymptotically equal for specific classes of holomorphic curves.

Findings

Reversion of the inequality in Cartan's theorem is possible.

A new theorem version approaches equality for solutions of linear differential equations.

The results apply to holomorphic curves in projective space.

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.