A packing problem for holomorphic curves

2006/05/13 by Masaki Tsukamoto, Tsukamoto, Masaki
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions #math.CV #math.DG #msc:32H30

paper · pdf · doi:10.48550/arxiv.math/0605353

33 pages

arxiv created 2006/05/13 · arxiv updated 2009/12/01

Abstract

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study the relation between theta functions and our packing problem. Applying the Nevanlinna theory, we investigate the packing densities of entire holomorphic curves in the complement of hyperplanes.

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