## The Equidistribution Theory of Holomorphic CurvesThis work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 A basic theorem on Integration over PC | 1 |

2 The fundamental inequality 152 | 122 |

3 The fundamental inequality of arbitrary rank | 170 |

4 Proof of the defect relations 180 | 208 |

### Common terms and phrases

Ahlfors arbitrary assume Chapter clearly Cn+1 compact Riemann surface compact set const coordinate neighborhood Corollary critical points CTk(r curvature form curve of rank ddc log defect relations defined definition denote dimensional projective discrete set dV[r dV[t dVTt dz Adz equal Euler characteristic F-S metric fact finite number fixed Gauss-Bonnet Theorem Gaussian curvature geodesic curvature h-dimensional projective subspace Hence hermitian metric holomorphic function holomorphic mapping hyperplanes implies induces inequality infinite harmonic exhaustion inner product integral integrand k-dimensional Lemma Let f lim sup log h meromorphic function nondegenerate nondegenerate holomorphic curve notation number of points open set order function order of zero orthogonal Picard's theorem polar divisor polar space positive constants Proof Recall reduced representation Riemann sphere stationary index subspace of PC Tk(r transcendental unit decomposable vector volume form X J A Xk J Ah