The Equidistribution Theory of Holomorphic Curves

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Princeton University Press, 1970 - Mathematics - 219 pages
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This 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.


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1 A basic theorem on Integration over PC
2 The fundamental inequality 152
3 The fundamental inequality of arbitrary rank
4 Proof of the defect relations 180

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